1
00:00:00,000 --> 00:00:06,653
สวัสดีค่ะ

2
00:00:07,040 --> 00:00:08,468
ให้พี่หล้าด้วยนะคะ

3
00:00:08,719 --> 00:00:09,175

4
00:00:08,907 --> 00:00:10,240
สวัสดีวันศุกร์ค่ะลูกๆ

5
00:00:10,376 --> 00:00:11,974

6
00:00:12,237 --> 00:00:12,477

7
00:00:12,557 --> 00:00:15,112
เป็นไงบ้างวันนี้วันศุกร์อากาศดีไหมคะ

8
00:00:16,721 --> 00:00:17,863

9
00:00:18,128 --> 00:00:19,585
อากาศดีไหมวันนี้

10
00:00:20,176 --> 00:00:22,425
หนาวไหม

11
00:00:22,549 --> 00:00:24,641
ไม่หนาวนะวันนี้น้องอากาศกำลังดี

12
00:00:24,812 --> 00:00:29,320
กำลังอาบน้ำสบายๆนะคะตื่นเช้ามาก็สดใสนะอากาศดี

13
00:00:29,401 --> 00:00:31,741
เดี๋ยวเรารอวีดีโอแป๊บนึงนะลูกนะ

14
00:00:33,431 --> 00:00:34,827
วันนี้เรา

15
00:00:34,839 --> 00:00:37,014
จะมาเรียนรู้หัวข้อใหม่

16
00:00:37,468 --> 00:00:39,640
แต่เนื้อหาก็ยังสืบเนื่องจาก

17
00:00:39,580 --> 00:00:40,666
เรื่องเดิมอยู่

18
00:00:41,568 --> 00:00:43,987
ถ้าใครยังจำ

19
00:00:43,999 --> 00:00:44,269

20
00:00:44,580 --> 00:00:47,396
ชั่วโมงที่แล้วที่เราเรียนกันได้นะคะเรื่องอะไรนะ

21
00:00:47,711 --> 00:00:48,542
อะไรคะ

22
00:00:48,480 --> 00:00:49,942
ลำดับใช่ไหม

23
00:00:49,898 --> 00:00:50,150

24
00:00:50,278 --> 00:00:50,491

25
00:00:50,990 --> 00:00:53,727
ลำดับใช่ไหมลูก

26
00:00:53,928 --> 00:00:54,167

27
00:00:54,121 --> 00:00:55,780
จำกันได้ไหมน้อ

28
00:00:56,171 --> 00:00:56,559

29
00:00:56,298 --> 00:00:57,110
ลำดับ

30
00:00:57,071 --> 00:00:57,561

31
00:00:57,328 --> 00:01:00,780
ให้เวลานะให้เวลาทบทวนนะคะลืมหมดแล้ว

32
00:01:00,719 --> 00:01:01,149

33
00:01:01,108 --> 00:01:04,289
ไม่เป็นไรเดี๋ยววันนี้คุณเจนจะมารบกวนนิดนึง

34
00:01:05,140 --> 00:01:09,136
เพราะหัวข้อที่เราจะเรียนมันซึมเนื่องจากเรื่องของลำดับด้วย

35
00:01:09,241 --> 00:01:09,495

36
00:01:09,559 --> 00:01:10,627

37
00:01:11,028 --> 00:01:11,593

38
00:01:11,550 --> 00:01:11,762

39
00:01:11,987 --> 00:01:12,270

40
00:01:13,600 --> 00:01:13,909

41
00:01:13,858 --> 00:01:14,135

42
00:01:14,108 --> 00:01:14,409

43
00:01:14,309 --> 00:01:14,617

44
00:01:14,630 --> 00:01:15,078

45
00:01:15,458 --> 00:01:15,866

46
00:01:15,650 --> 00:01:18,724
รอสักพักนึงนะลูกรอแป๊บนึง

47
00:01:18,980 --> 00:01:19,214

48
00:01:20,831 --> 00:01:21,109

49
00:01:21,349 --> 00:01:22,163

50
00:01:22,187 --> 00:01:22,408

51
00:01:22,437 --> 00:01:22,806

52
00:01:23,019 --> 00:01:27,688
วันนี้นะคะเราจะมาเรียนในเรื่องของอนุกรม

53
00:01:27,750 --> 00:01:28,841
จะได้ยินไหม

54
00:01:28,968 --> 00:01:30,116
อนุกรม

55
00:01:31,091 --> 00:01:32,659
ไม่เคยได้ยินคำนี้ลูก

56
00:01:32,560 --> 00:01:32,852

57
00:01:34,161 --> 00:01:35,073
ไม่เคยเนาะ

58
00:01:35,630 --> 00:01:36,335

59
00:01:36,340 --> 00:01:36,574

60
00:01:36,791 --> 00:01:40,272
แปลกนะลูกวิชาคณิตศาสตร์มันก็จะมีศัพท์เฉพาะของมันเยอะแยะเลย

61
00:01:40,759 --> 00:01:41,071

62
00:01:41,791 --> 00:01:42,860
อนุกรม

63
00:01:42,940 --> 00:01:46,179
วันนี้เราจะมาเรียนรู้ในเรื่องความหมายของอนุกรมกันนะคะ

64
00:01:46,139 --> 00:01:46,409

65
00:01:46,340 --> 00:01:46,604

66
00:01:48,960 --> 00:01:49,797

67
00:01:50,427 --> 00:01:51,074

68
00:01:51,070 --> 00:01:51,392

69
00:01:51,327 --> 00:01:51,708

70
00:01:51,970 --> 00:01:52,357

71
00:01:52,289 --> 00:01:52,746

72
00:01:52,742 --> 00:01:53,047

73
00:01:53,441 --> 00:01:58,716
โอเคอ่านในเรื่องอนุกรมวันนี้นะคะจุดประสงค์หลักๆที่

74
00:01:58,700 --> 00:02:00,921
เมื่อเราเรียนจบกับคุณเจนแล้วเนี่ย

75
00:02:01,583 --> 00:02:06,507
ลูกๆทุกคนต้องเข้าใจหรือว่าต้องสามารถทำได้นะคะอันแรกเลย

76
00:02:06,904 --> 00:02:07,324

77
00:02:07,149 --> 00:02:08,483
ลูกๆนะคะ

78
00:02:08,819 --> 00:02:11,379
สามารถอธิบายความหมายของอนุกรมได้

79
00:02:11,318 --> 00:02:11,717

80
00:02:11,960 --> 00:02:13,364
อนุกรมมันคืออะไร

81
00:02:13,817 --> 00:02:16,334
เรียนจบแล้วนี่ต้องเข้าใจตรงนี้เลยนะ

82
00:02:16,699 --> 00:02:17,391

83
00:02:17,788 --> 00:02:22,591
ข้อ 2 นะคะลูกๆสามารถเข้าใจความหมายของผลบวก

84
00:02:22,660 --> 00:02:23,507
มด

85
00:02:23,997 --> 00:02:26,484
n พจน์แรกของอนุกรมได้

86
00:02:28,297 --> 00:02:30,246
พจน์แรกของอนุกรมนะ

87
00:02:30,727 --> 00:02:32,414
ข้อสุดท้ายนะคะ

88
00:02:32,460 --> 00:02:37,883
นักเรียนสามารถหรือว่าลูกๆเนี่ยสามารถหาผลบวกของ N พจน์แรกของอนุกรม

89
00:02:37,648 --> 00:02:38,470
ผมได้

90
00:02:38,669 --> 00:02:40,842
คือหาผลบวกของ N พจน์แรกได้

91
00:02:41,357 --> 00:02:41,749

92
00:02:41,806 --> 00:02:42,235

93
00:02:44,057 --> 00:02:46,837
ขึ้นกระดานใช่ไหมคะเนี่ย

94
00:02:46,749 --> 00:02:48,070

95
00:02:48,278 --> 00:02:48,796

96
00:02:48,727 --> 00:02:49,542

97
00:02:51,288 --> 00:02:51,559

98
00:02:51,607 --> 00:02:54,495
โอเคขึ้นกระดานก็ได้สรุป

99
00:02:54,518 --> 00:02:55,951

100
00:02:55,905 --> 00:02:56,164

101
00:02:56,159 --> 00:02:56,424

102
00:02:56,480 --> 00:02:56,786

103
00:02:56,737 --> 00:02:57,420

104
00:02:57,436 --> 00:02:57,947

105
00:02:58,017 --> 00:02:59,025

106
00:02:59,297 --> 00:03:02,500
มาดูความหมายของอนุกรมก่อนนะคะ

107
00:03:02,758 --> 00:03:03,040

108
00:03:03,267 --> 00:03:03,832

109
00:03:04,036 --> 00:03:07,360
อนุกรมอนุกรมคืออะไร

110
00:03:07,368 --> 00:03:07,815

111
00:03:08,141 --> 00:03:08,353

112
00:03:08,717 --> 00:03:08,955

113
00:03:09,747 --> 00:03:10,439

114
00:03:10,387 --> 00:03:10,954

115
00:03:10,958 --> 00:03:13,714
อนุกรมนะคะคือผลบวกของลำดับ

116
00:03:13,712 --> 00:03:14,027

117
00:03:14,742 --> 00:03:16,355
ความหมายง่ายๆสั้นๆลูก

118
00:03:16,541 --> 00:03:17,420
ผล

119
00:03:17,497 --> 00:03:18,199
+

120
00:03:18,520 --> 00:03:19,732
ของ

121
00:03:20,309 --> 00:03:22,344
ลำดับ

122
00:03:22,489 --> 00:03:23,375

123
00:03:23,446 --> 00:03:23,736

124
00:03:23,958 --> 00:03:24,376

125
00:03:24,348 --> 00:03:25,029

126
00:03:24,988 --> 00:03:27,290
ในหัวข้อนี้

127
00:03:27,296 --> 00:03:27,585

128
00:03:27,489 --> 00:03:30,020
ควรต้องสอนเรื่องการบวกเลข

129
00:03:30,107 --> 00:03:30,317

130
00:03:30,425 --> 00:03:32,415
เตรียมความพร้อม

131
00:03:32,477 --> 00:03:34,986
เผื่อมีการแข่งขันอะไรนะคะเราจะได้

132
00:03:34,857 --> 00:03:36,131
เตรียมตัวได้เนาะ

133
00:03:36,138 --> 00:03:36,419

134
00:03:37,419 --> 00:03:42,575
อนุกรมก็คือผลบวกของลำดับนะคะเช่น

135
00:03:43,251 --> 00:03:44,422
ดูด้วยนะ

136
00:03:44,716 --> 00:03:47,163
เช่นระดับ 1

137
00:03:47,355 --> 00:03:48,243
3

138
00:03:48,316 --> 00:03:49,227
5

139
00:03:49,347 --> 00:03:49,739

140
00:03:50,179 --> 00:03:50,808

141
00:03:51,267 --> 00:03:51,565

142
00:03:51,648 --> 00:03:53,458
ลำดับจำได้ไหม

143
00:03:53,436 --> 00:03:53,912

144
00:03:53,760 --> 00:03:55,707
อันนี้คือรูปแบบของลำดับใช่ไหมคะ

145
00:03:56,200 --> 00:04:01,469
อนุกรมของลำดับนี้นะคะอนุกรมของลำดับนี้

146
00:04:01,839 --> 00:04:02,724
เสือลาย

147
00:04:06,896 --> 00:04:08,671
คืออะไรคะ

148
00:04:11,894 --> 00:04:14,902
แสดงว่าลำดับ 1 3 5 7 9

149
00:04:15,358 --> 00:04:18,476
อนุกรมของลำดับนี้ก็คืออะไรคะคือ 1

150
00:04:18,489 --> 00:04:19,421
หมวก

151
00:04:20,218 --> 00:04:21,298
3

152
00:04:21,441 --> 00:04:22,453
+

153
00:04:22,851 --> 00:04:24,565
+

154
00:04:24,638 --> 00:04:26,110
เจ็บแล้วก็บวก

155
00:04:26,176 --> 00:04:26,871

156
00:04:27,326 --> 00:04:28,405

157
00:04:28,547 --> 00:04:28,841

158
00:04:28,931 --> 00:04:30,843
มีค่าเท่าไหร่

159
00:04:30,855 --> 00:04:31,141

160
00:04:31,687 --> 00:04:34,708
อนุกรมนี้มีค่าเท่าไหร่คะก็นำตัวเลขมาบวกกัน

161
00:04:35,787 --> 00:04:37,130
นำตัวเลขบวกกัน

162
00:04:37,069 --> 00:04:37,358

163
00:04:37,316 --> 00:04:37,678

164
00:04:37,635 --> 00:04:37,883

165
00:04:37,766 --> 00:04:39,899
1020

166
00:04:39,827 --> 00:04:40,041

167
00:04:40,399 --> 00:04:42,980
พี่ลองบอกสิลูก 1 + 3

168
00:04:43,797 --> 00:04:44,995
1 + 3

169
00:04:45,839 --> 00:04:46,849

170
00:04:46,880 --> 00:04:50,896
1 + 3

171
00:04:50,966 --> 00:04:51,589

172
00:04:51,995 --> 00:04:53,710
บวกเพิ่มอีก 3

173
00:04:54,038 --> 00:04:54,722

174
00:04:54,876 --> 00:05:00,232
cn4 ใช่หรอกางเกง 4 + 5

175
00:05:00,067 --> 00:05:00,948

176
00:05:01,219 --> 00:05:03,318
4 + 5

177
00:05:03,526 --> 00:05:04,406

178
00:05:06,406 --> 00:05:09,221
4 + 5 เท่าไหร่ลูก 4 + 5

179
00:05:09,286 --> 00:05:10,232
4

180
00:05:10,506 --> 00:05:12,987
r9

181
00:05:13,007 --> 00:05:14,865
สบาย 9 + 7

182
00:05:15,317 --> 00:05:15,566

183
00:05:15,569 --> 00:05:18,503
99 +

184
00:05:18,705 --> 00:05:19,286

185
00:05:19,406 --> 00:05:20,554
9

186
00:05:21,527 --> 00:05:24,789
9 + เจ็บ

187
00:05:25,234 --> 00:05:28,052
16 เก่งมาก

188
00:05:28,066 --> 00:05:30,045
16 + 9 ค่ะ

189
00:05:29,986 --> 00:05:31,466
10

190
00:05:31,396 --> 00:05:32,202

191
00:05:32,228 --> 00:05:33,305
+

192
00:05:33,435 --> 00:05:33,678

193
00:05:33,696 --> 00:05:35,343

194
00:05:35,877 --> 00:05:37,583

195
00:05:38,116 --> 00:05:38,893

196
00:05:38,888 --> 00:05:41,642
6 + 9

197
00:05:42,087 --> 00:05:49,782
2525 ถูกต้องค่ะ

198
00:05:50,415 --> 00:05:51,682
25

199
00:05:51,825 --> 00:05:52,714

200
00:05:52,726 --> 00:05:55,161
อนุกรมของลำดับนี้ก็คืออะไรคะ

201
00:05:55,356 --> 00:05:55,598

202
00:05:55,927 --> 00:05:56,181

203
00:05:56,374 --> 00:05:57,707
25

204
00:05:58,489 --> 00:05:59,365
ได้ไหม

205
00:06:00,217 --> 00:06:01,116
ได้ไหมคะ

206
00:06:01,829 --> 00:06:02,842
ได้ไหม

207
00:06:03,106 --> 00:06:03,875

208
00:06:03,997 --> 00:06:04,969
เข้าใจไหมคะ

209
00:06:04,954 --> 00:06:05,418

210
00:06:05,217 --> 00:06:11,691
อนุกรมคือผลบวกของลำดับถ้าเรามีลำดับขึ้นมาแบบนี้นะคะเราสามารถเขียนรูป

211
00:06:11,306 --> 00:06:11,939

212
00:06:12,197 --> 00:06:15,218
อนุกรมลำดับนี้ได้เลยก็คือนำตัวเลขมา

213
00:06:15,465 --> 00:06:16,149
+

214
00:06:16,164 --> 00:06:16,696

215
00:06:16,746 --> 00:06:17,269

216
00:06:17,196 --> 00:06:21,149
บวกกันไปเรื่อยๆถูกไหมคะอยู่ที่ว่าลำดับนั้นมีกี่พจน์ใช่ไหมลูก

217
00:06:21,484 --> 00:06:22,308
ใช่ไหม

218
00:06:22,764 --> 00:06:25,121
พี่นิ

219
00:06:25,145 --> 00:06:25,644

220
00:06:25,714 --> 00:06:26,920
มาดูต่อ

221
00:06:27,315 --> 00:06:27,570

222
00:06:27,764 --> 00:06:28,321

223
00:06:28,277 --> 00:06:28,552

224
00:06:28,475 --> 00:06:28,828

225
00:06:29,115 --> 00:06:29,570

226
00:06:29,494 --> 00:06:29,739

227
00:06:29,757 --> 00:06:30,107

228
00:06:30,075 --> 00:06:30,928

229
00:06:30,907 --> 00:06:33,392
ในหัวข้อนี้เราจะกำหนดนะคะ

230
00:06:34,306 --> 00:06:36,241
FM นะคะลูก

231
00:06:36,225 --> 00:06:36,440

232
00:06:36,926 --> 00:06:37,355

233
00:06:37,957 --> 00:06:39,418
sn

234
00:06:40,894 --> 00:06:43,476
มีตัวแปรใหม่มาให้เราเห็นอีกละ

235
00:06:43,468 --> 00:06:46,598
sn นะคะแทนผลบวก

236
00:06:46,474 --> 00:06:46,789

237
00:06:48,906 --> 00:06:49,208

238
00:06:49,748 --> 00:06:51,281
Tan ผลบวก

239
00:06:51,916 --> 00:06:52,991
นะคะ

240
00:06:52,944 --> 00:06:53,261

241
00:06:54,097 --> 00:06:54,349

242
00:06:54,286 --> 00:06:55,691
n พจน์แรกของลำดับ

243
00:06:58,078 --> 00:06:58,300

244
00:06:58,904 --> 00:06:59,167

245
00:06:59,097 --> 00:06:59,391

246
00:06:59,415 --> 00:06:59,701

247
00:07:00,633 --> 00:07:01,117

248
00:07:02,615 --> 00:07:02,894

249
00:07:02,996 --> 00:07:03,271

250
00:07:03,706 --> 00:07:06,603
หรือพูดง่ายๆว่า sn ในรูปแทนอนุกรม

251
00:07:07,295 --> 00:07:07,933

252
00:07:08,196 --> 00:07:09,713
เขียนแทนอนุกรม

253
00:07:10,045 --> 00:07:11,691
ได้เลยนะคะ

254
00:07:11,907 --> 00:07:12,327

255
00:07:12,996 --> 00:07:13,233

256
00:07:13,185 --> 00:07:16,954
งั้นถ้าเราเขียนตัวนี้ใช่ไหมคะเราจะได้ว่า sn

257
00:07:17,226 --> 00:07:18,117
เท่ากับ

258
00:07:21,063 --> 00:07:22,630
บทที่ 1 ใช่ไหม

259
00:07:22,862 --> 00:07:26,166
ที่ 1 + พจน์ที่ 2

260
00:07:26,257 --> 00:07:27,022
+

261
00:07:27,026 --> 00:07:29,209
บทที่ 3

262
00:07:29,966 --> 00:07:31,310
บวกไปเรื่อยๆ

263
00:07:31,443 --> 00:07:31,884

264
00:07:32,086 --> 00:07:33,105
ถึงอะไรคะ

265
00:07:33,873 --> 00:07:34,929
พจน์ที่ n

266
00:07:35,473 --> 00:07:35,856

267
00:07:35,993 --> 00:07:36,290

268
00:07:36,245 --> 00:07:36,523

269
00:07:36,823 --> 00:07:39,902
ในตัวอย่างนี้ก็คือ 1 บวกอะไรคะ

270
00:07:40,153 --> 00:07:41,155
3

271
00:07:41,186 --> 00:07:42,321
+ 5

272
00:07:42,273 --> 00:07:42,996
+7

273
00:07:43,353 --> 00:07:44,661
+ ป้าง

274
00:07:45,024 --> 00:07:45,587

275
00:07:45,597 --> 00:07:47,459
มาแล้วค่ะได้เท่าไหร่คะ

276
00:07:48,616 --> 00:07:52,184
25 ใช่ไหม

277
00:07:52,265 --> 00:07:55,382
วันนี้เราจะเห็นนะคะจำไว้เลยนะต่อไปนี้เราจะ

278
00:07:55,475 --> 00:07:56,048

279
00:07:56,177 --> 00:07:57,455
คุ้นเคยกับ

280
00:07:57,394 --> 00:07:57,873

281
00:07:57,833 --> 00:07:58,855
sn

282
00:07:59,314 --> 00:08:00,067
เท่ากับ

283
00:08:00,076 --> 00:08:03,306
A1 + A2 + A3 + ไปเรื่อยๆจนถึง

284
00:08:03,155 --> 00:08:04,230

285
00:08:04,314 --> 00:08:04,771

286
00:08:04,562 --> 00:08:04,777

287
00:08:04,694 --> 00:08:05,640

288
00:08:05,713 --> 00:08:06,016

289
00:08:06,233 --> 00:08:06,451

290
00:08:06,358 --> 00:08:06,582

291
00:08:06,874 --> 00:08:08,589

292
00:08:08,664 --> 00:08:09,347

293
00:08:09,624 --> 00:08:12,170

294
00:08:12,313 --> 00:08:15,187
ที่นี้นะคะว่าถึงตรงนี้

295
00:08:15,264 --> 00:08:17,517
ฉันก็จะยอมเป็นเรื่องของลำดับ

296
00:08:17,503 --> 00:08:18,086

297
00:08:18,466 --> 00:08:20,372
จำได้ไหมว่าลำดับมีกี่

298
00:08:20,645 --> 00:08:21,728
กี่ประเภทคะ

299
00:08:22,242 --> 00:08:24,222
ลำดับจำได้ไหม

300
00:08:24,165 --> 00:08:25,858
น้ำหนักมีอยู่ 2

301
00:08:25,764 --> 00:08:26,920
ประเภท

302
00:08:27,944 --> 00:08:28,959
นึกออกไหมคะ

303
00:08:28,916 --> 00:08:30,701
อันแรกคือลำดับจำกัด

304
00:08:31,152 --> 00:08:32,103
ใช่ไหม

305
00:08:32,173 --> 00:08:36,444
ลำดับจำกัดก็คือลำดับที่เรารู้ว่ามันมีกี่คน

306
00:08:36,796 --> 00:08:37,097

307
00:08:37,173 --> 00:08:37,445

308
00:08:37,687 --> 00:08:37,961

309
00:08:38,004 --> 00:08:40,686
ใช่ไหมคะ

310
00:08:40,633 --> 00:08:41,020

311
00:08:40,953 --> 00:08:41,264

312
00:08:41,525 --> 00:08:43,644
ลำดับที่มี A1

313
00:08:43,953 --> 00:08:44,265

314
00:08:44,733 --> 00:08:46,138
A2

315
00:08:46,074 --> 00:08:46,354

316
00:08:46,464 --> 00:08:48,715
A3 ไปเรื่อยๆ

317
00:08:49,476 --> 00:08:51,273
เอเลน

318
00:08:51,132 --> 00:08:52,545
จบที่เอน

319
00:08:52,475 --> 00:08:54,740
นั่นหมายถึงว่าลำดับนี้มี

320
00:08:54,984 --> 00:08:56,378
ยูเวนตุส

321
00:08:56,459 --> 00:08:58,121
ใช่ไหมคะอันนี้เขาเรียกว่าลำดับ

322
00:08:58,435 --> 00:08:59,099
จำกัด

323
00:08:59,012 --> 00:08:59,225

324
00:08:59,143 --> 00:08:59,422

325
00:08:59,394 --> 00:09:02,219
ถ้าเรานำลำดับจำกัดนี้มาเขียน

326
00:09:02,673 --> 00:09:03,882
อนุกรม

327
00:09:04,523 --> 00:09:06,502
เราก็จะได้ว่า

328
00:09:06,442 --> 00:09:06,677

329
00:09:08,366 --> 00:09:13,311
A1 + A2 + A3 และบวกไปเรื่อยๆถึง

330
00:09:13,304 --> 00:09:14,117

331
00:09:14,649 --> 00:09:16,896
เราจะเรียกว่าอนุกรมจำกัด

332
00:09:16,883 --> 00:09:17,125

333
00:09:18,302 --> 00:09:18,580

334
00:09:19,196 --> 00:09:20,725
ที่ร้านนะคะ

335
00:09:20,924 --> 00:09:24,501
มีร้านนะตรงนี้ต้องเข้าใจแล้วต้องจำด้วย

336
00:09:24,895 --> 00:09:26,362

337
00:09:26,953 --> 00:09:28,493
ที่นี้เหมือนกันค่ะ

338
00:09:28,802 --> 00:09:32,748
ลำดับ 1 ลำดับที่ 2 คือลำดับอนันต์

339
00:09:34,444 --> 00:09:38,970
ลำดับอนันต์ก็คือลำดับที่เราไม่รู้เลยว่าโพสต์นั้นมีกี่

340
00:09:39,113 --> 00:09:39,821

341
00:09:39,959 --> 00:09:40,247

342
00:09:40,783 --> 00:09:42,972
มันมีกี่พจน์เราไม่รู้

343
00:09:42,832 --> 00:09:43,123

344
00:09:43,224 --> 00:09:45,733
มันจะเขียนในรูปของ A 1 +

345
00:09:45,654 --> 00:09:49,294
A2 + A3 + ไปเรื่อยๆจนถึง

346
00:09:49,812 --> 00:09:50,943
KN

347
00:09:51,035 --> 00:09:51,274

348
00:09:51,163 --> 00:09:53,708
และยังมีบวกต่อไปอีก

349
00:09:54,304 --> 00:09:56,021
Infinity ไม่มีที่สิ้นสุด

350
00:09:55,965 --> 00:09:56,256

351
00:09:56,604 --> 00:09:58,068
แบบนั้นเราเรียกว่า

352
00:09:59,304 --> 00:10:05,118
ลำดับอนันต์และลำดับอนันต์นะคะมาเขียนเป็นอนุกรมมันก็จะได้เป็น

353
00:10:05,384 --> 00:10:06,851
อนุกรมอนันต์

354
00:10:07,052 --> 00:10:07,531

355
00:10:07,564 --> 00:10:09,089
ระวังนะคะ

356
00:10:09,232 --> 00:10:09,524

357
00:10:09,422 --> 00:10:09,790

358
00:10:10,513 --> 00:10:10,760

359
00:10:10,634 --> 00:10:11,068

360
00:10:11,022 --> 00:10:11,450

361
00:10:11,471 --> 00:10:11,902

362
00:10:12,043 --> 00:10:12,263

363
00:10:12,301 --> 00:10:12,619

364
00:10:12,552 --> 00:10:12,763

365
00:10:13,583 --> 00:10:18,324
ไม่เข้าใจอ่ะที่นี้พอถึงตรงนี้เราสามารถสรุปได้ว่า

366
00:10:18,645 --> 00:10:18,923

367
00:10:19,475 --> 00:10:19,730

368
00:10:19,674 --> 00:10:21,132
อนุกรมจำกัด

369
00:10:21,076 --> 00:10:22,860
มาจากลำดับจำกัด

370
00:10:23,075 --> 00:10:24,212
ไหมคะ

371
00:10:24,356 --> 00:10:26,835
อนุกรมอนันต์ก็มาจากลำดับ

372
00:10:27,108 --> 00:10:28,186
อนันต์

373
00:10:28,383 --> 00:10:29,211

374
00:10:29,153 --> 00:10:30,108

375
00:10:30,043 --> 00:10:31,467

376
00:10:31,842 --> 00:10:32,049

377
00:10:32,993 --> 00:10:33,706

378
00:10:33,635 --> 00:10:33,905

379
00:10:33,832 --> 00:10:34,069

380
00:10:34,156 --> 00:10:37,184
โอเคนะมาถึงตัวนี้นะคะเดี๋ยว

381
00:10:37,154 --> 00:10:41,669
อุปสงค์ต่อไปคือเรื่องการบวก n พจน์แรกของอนุกรม

382
00:10:42,154 --> 00:10:47,377
โดจินขออนุญาตลบกระดานแป๊บนึง

383
00:10:47,214 --> 00:10:47,471

384
00:10:48,953 --> 00:10:49,763

385
00:10:49,715 --> 00:10:50,203

386
00:10:50,671 --> 00:10:50,902

387
00:10:51,702 --> 00:10:53,866

388
00:10:53,871 --> 00:10:54,628

389
00:10:54,582 --> 00:10:54,824

390
00:10:54,714 --> 00:10:54,937

391
00:10:54,964 --> 00:10:55,457

392
00:10:55,602 --> 00:10:55,849

393
00:10:55,744 --> 00:10:56,021

394
00:10:55,993 --> 00:10:56,748

395
00:10:57,022 --> 00:10:57,235

396
00:10:58,364 --> 00:10:58,607

397
00:10:58,870 --> 00:10:59,152

398
00:10:59,321 --> 00:10:59,561

399
00:10:59,451 --> 00:10:59,684

400
00:11:01,882 --> 00:11:02,111

401
00:11:02,072 --> 00:11:02,494

402
00:11:02,914 --> 00:11:07,915
ปีนี้เราจะมาหาผลบวก n พจน์แรกนะคะของอนุกรมกัน

403
00:11:08,032 --> 00:11:08,250

404
00:11:08,422 --> 00:11:08,782

405
00:11:09,574 --> 00:11:11,879
ถามก่อนใครตอบได้

406
00:11:11,874 --> 00:11:12,638

407
00:11:12,712 --> 00:11:14,428
อนุกรมคืออะไรนะ

408
00:11:15,403 --> 00:11:19,521
มหานาทีที่แล้วคุณเจนพูดไปแล้วอนุกรมคืออะไรนะคะใครตอบได้

409
00:11:19,631 --> 00:11:20,470
ขอได้ไหม

410
00:11:20,592 --> 00:11:21,861
อนุกรมคือ

411
00:11:22,711 --> 00:11:22,950

412
00:11:23,092 --> 00:11:23,318

413
00:11:23,222 --> 00:11:23,515

414
00:11:23,543 --> 00:11:25,434
อนุกรมคือ

415
00:11:25,391 --> 00:11:25,633

416
00:11:25,591 --> 00:11:25,825

417
00:11:26,742 --> 00:11:29,134
อนุกรมคืออะไรคะจำได้ไหม

418
00:11:33,403 --> 00:11:34,646
ดำ

419
00:11:35,074 --> 00:11:35,292

420
00:11:35,190 --> 00:11:37,629
อนุกรมคืออะไรใครตอบได้บ้าง

421
00:11:37,954 --> 00:11:39,485
คือผลบวกอะไรนะ

422
00:11:40,641 --> 00:11:41,159

423
00:11:41,352 --> 00:11:43,447
อนุกรมคือผลบวกของ

424
00:11:43,782 --> 00:11:44,023

425
00:11:44,033 --> 00:11:44,258

426
00:11:45,263 --> 00:11:45,560

427
00:11:45,514 --> 00:11:45,754

428
00:11:45,770 --> 00:11:47,307
ตอบหน่อยตอบหน่อย

429
00:11:47,243 --> 00:11:47,442

430
00:11:47,371 --> 00:11:49,415
อนุกรมคือผลบวกของ

431
00:11:49,482 --> 00:11:50,827
ของอะไรคะ

432
00:11:51,021 --> 00:11:51,961
ท้อง

433
00:11:52,751 --> 00:11:53,897
ของลำดับ

434
00:11:53,844 --> 00:11:54,155

435
00:11:54,994 --> 00:11:56,583
น้ำหนักคือตัวเลขถูกไหม

436
00:11:56,405 --> 00:11:56,655

437
00:11:57,043 --> 00:11:58,713
ของลำดับ

438
00:11:58,644 --> 00:12:00,871
อนุกรมคือผลบวกของลำดับ

439
00:12:01,010 --> 00:12:01,307

440
00:12:01,531 --> 00:12:04,402
งั้นวันนี้ถ้ากำหนดให้นะคะ

441
00:12:04,355 --> 00:12:05,168

442
00:12:05,180 --> 00:12:05,759
วันนี้

443
00:12:05,692 --> 00:12:08,634
ตัวอย่างนะถ้ากำหนดให้

444
00:12:08,759 --> 00:12:09,196

445
00:12:09,273 --> 00:12:09,664

446
00:12:09,673 --> 00:12:10,173

447
00:12:10,631 --> 00:12:10,861

448
00:12:10,954 --> 00:12:12,745
แนวนี้กำหนดให้

449
00:12:12,803 --> 00:12:13,072

450
00:12:13,311 --> 00:12:14,465
School

451
00:12:14,472 --> 00:12:14,976

452
00:12:15,234 --> 00:12:15,663

453
00:12:15,809 --> 00:12:16,054

454
00:12:16,003 --> 00:12:16,818

455
00:12:16,902 --> 00:12:19,335
วันนี้ถ้าเกินกำหนดให้

456
00:12:19,271 --> 00:12:19,766

457
00:12:20,684 --> 00:12:21,106

458
00:12:21,132 --> 00:12:21,496

459
00:12:21,513 --> 00:12:21,746

460
00:12:22,603 --> 00:12:23,168

461
00:12:23,116 --> 00:12:24,451

462
00:12:25,291 --> 00:12:25,575

463
00:12:25,671 --> 00:12:27,336
ลำดับของ

464
00:12:27,794 --> 00:12:28,033

465
00:12:28,820 --> 00:12:31,516
357

466
00:12:31,632 --> 00:12:31,933

467
00:12:32,021 --> 00:12:33,937
9

468
00:12:33,870 --> 00:12:34,123

469
00:12:34,521 --> 00:12:34,780

470
00:12:34,914 --> 00:12:35,266

471
00:12:35,872 --> 00:12:36,088

472
00:12:36,119 --> 00:12:36,371

473
00:12:36,313 --> 00:12:36,867

474
00:12:36,950 --> 00:12:39,930
นักเรียนสามารถหาผลบวกของอนุกรมนี้ได้ไหมคะ

475
00:12:40,792 --> 00:12:41,674

476
00:12:42,273 --> 00:12:44,640
ได้อย่างนี้นะคะเราเขียน

477
00:12:44,830 --> 00:12:46,627
ตัวแปร sn

478
00:12:47,141 --> 00:12:50,112
YSS ตัวแรกที่กูจะบอกให้จำไม่ได้นะ

479
00:12:50,022 --> 00:12:51,544
sn =

480
00:12:51,955 --> 00:12:55,009
A1 + A2 +

481
00:12:55,081 --> 00:12:57,524
A3 บวกไปเรื่อยๆถึง

482
00:12:57,640 --> 00:12:58,704
a n

483
00:12:58,741 --> 00:13:00,064
อยู่ที่ว่า

484
00:13:01,041 --> 00:13:02,985
อนุกรมนั้นมีกี่พจน์ใช่ไหม

485
00:13:03,091 --> 00:13:05,778
อนุกรมที่มีการกำหนดให้มีกี่คนคะ

486
00:13:07,134 --> 00:13:08,224
ช่วยกันตอบหน่อย

487
00:13:09,431 --> 00:13:09,684

488
00:13:09,821 --> 00:13:11,793
ตัวนี้มีกี่พจน์

489
00:13:11,990 --> 00:13:12,257

490
00:13:12,313 --> 00:13:12,537

491
00:13:12,633 --> 00:13:13,339

492
00:13:13,914 --> 00:13:14,664

493
00:13:14,692 --> 00:13:14,969

494
00:13:14,940 --> 00:13:15,764

495
00:13:15,912 --> 00:13:16,816
2

496
00:13:17,189 --> 00:13:18,018
3

497
00:13:18,081 --> 00:13:18,373

498
00:13:18,470 --> 00:13:21,440
4 ใช่ลำดับตอนนี้มีแค่

499
00:13:21,540 --> 00:13:22,499
สีพ้น

500
00:13:22,432 --> 00:13:24,576
ว่าเราจะเขียนผลบวกของ

501
00:13:24,869 --> 00:13:27,902
ลำดับนี้นะคะหรืออนุกรมไม่ได้เป็นอะไรคะ

502
00:13:28,141 --> 00:13:29,572
N A 1 +

503
00:13:29,613 --> 00:13:32,631
A2 + A3 และ + แค่อะไรคะ

504
00:13:33,329 --> 00:13:33,949

505
00:13:34,099 --> 00:13:34,725

506
00:13:34,991 --> 00:13:36,017
ใช่ไหม

507
00:13:36,529 --> 00:13:38,025
เพราะมันมีแค่ 4

508
00:13:38,579 --> 00:13:39,741
4

509
00:13:40,062 --> 00:13:40,338

510
00:13:40,311 --> 00:13:43,628
มาแล้วมาเขียนผลบวกด้วยค่ะ 1 คืออะไร

511
00:13:43,831 --> 00:13:45,371
ตอบได้ A1 คือ

512
00:13:48,071 --> 00:13:49,021

513
00:13:49,152 --> 00:13:49,420

514
00:13:49,733 --> 00:13:50,042

515
00:13:50,429 --> 00:13:50,996

516
00:13:51,140 --> 00:13:51,577

517
00:13:51,590 --> 00:13:51,825

518
00:13:51,972 --> 00:13:54,008
มองเห็นไหมนั่นคืออะไรคะ

519
00:13:54,659 --> 00:13:58,401
13 13 ถูกต้องค่ะ

520
00:13:58,511 --> 00:13:59,676
ที่ 2 นะคะ

521
00:14:00,040 --> 00:14:02,932
เยี่ยมมาก S3

522
00:14:04,070 --> 00:14:09,289
เทพสุดท้าย FC คือ

523
00:14:09,519 --> 00:14:09,828

524
00:14:10,549 --> 00:14:11,500
แล้วก็นำ

525
00:14:11,699 --> 00:14:12,380

526
00:14:12,469 --> 00:14:16,808
กันดูนะคะบวกอันตรายช่วยกัน

527
00:14:16,891 --> 00:14:17,251

528
00:14:17,719 --> 00:14:19,189
3 + 5

529
00:14:19,195 --> 00:14:19,586

530
00:14:19,711 --> 00:14:19,941

531
00:14:20,412 --> 00:14:20,658

532
00:14:20,669 --> 00:14:20,927

533
00:14:20,929 --> 00:14:21,676

534
00:14:21,829 --> 00:14:24,382
88 + 7

535
00:14:25,223 --> 00:14:25,698

536
00:14:25,792 --> 00:14:28,067
คิดเลขเร็วเร็ว

537
00:14:28,107 --> 00:14:30,064
ซ้อมไว้ซ้อมไว้

538
00:14:30,410 --> 00:14:31,373
เท่าไหร่

539
00:14:31,949 --> 00:14:32,247

540
00:14:32,272 --> 00:14:32,783

541
00:14:33,353 --> 00:14:33,783

542
00:14:33,801 --> 00:14:34,051

543
00:14:34,059 --> 00:14:37,192
15 และ 15 + 9

544
00:14:37,590 --> 00:14:38,463

545
00:14:38,422 --> 00:14:39,001

546
00:14:38,990 --> 00:14:39,251

547
00:14:39,256 --> 00:14:40,016

548
00:14:40,153 --> 00:14:40,855

549
00:14:40,852 --> 00:14:41,101

550
00:14:41,170 --> 00:14:41,596

551
00:14:42,131 --> 00:14:44,809
15 + 9

552
00:14:44,820 --> 00:14:45,244

553
00:14:45,401 --> 00:14:45,785

554
00:14:46,232 --> 00:14:46,457

555
00:14:46,431 --> 00:14:51,358
524 เก่งมากนะคะ 24

556
00:14:51,738 --> 00:14:51,999

557
00:14:51,931 --> 00:14:52,300

558
00:14:52,250 --> 00:14:53,060
นั้น

559
00:14:53,601 --> 00:14:53,963

560
00:14:54,111 --> 00:14:54,342

561
00:14:54,375 --> 00:14:54,813

562
00:14:54,881 --> 00:14:57,903
ลำดับของ 3579 นะคะ

563
00:14:58,718 --> 00:15:02,688
เราสามารถเขียนเป็นอนุกรมหาผลบวกของ

564
00:15:02,630 --> 00:15:04,633
ระดับนี้ได้นะคะคือเท่าไหร่

565
00:15:04,943 --> 00:15:05,946
24

566
00:15:06,919 --> 00:15:09,596
อนุกรมตัวนี้มีค่าเท่ากับเท่าไหร่คะ

567
00:15:09,673 --> 00:15:11,092
24 นางเอก

568
00:15:11,861 --> 00:15:12,165

569
00:15:12,048 --> 00:15:12,320

570
00:15:12,560 --> 00:15:13,769

571
00:15:13,779 --> 00:15:14,102

572
00:15:14,099 --> 00:15:17,489
เข้าใจไหมโอเคเข้าใจถ้าเข้าใจมีโจทย์ให้ทำ

573
00:15:17,679 --> 00:15:17,899

574
00:15:17,998 --> 00:15:19,232
ง่ายๆนี้ก่อน

575
00:15:19,613 --> 00:15:19,921

576
00:15:20,441 --> 00:15:23,260
ได้ๆนี่ก่อนเริ่มจากง่ายๆก่อนนะ

577
00:15:23,509 --> 00:15:23,744

578
00:15:23,771 --> 00:15:24,135

579
00:15:24,540 --> 00:15:24,837

580
00:15:25,629 --> 00:15:25,945

581
00:15:27,042 --> 00:15:27,865

582
00:15:28,001 --> 00:15:28,619

583
00:15:28,708 --> 00:15:28,940

584
00:15:30,108 --> 00:15:30,346

585
00:15:31,137 --> 00:15:31,497

586
00:15:31,709 --> 00:15:31,995

587
00:15:32,551 --> 00:15:32,827

588
00:15:32,931 --> 00:15:33,937

589
00:15:34,208 --> 00:15:35,096

590
00:15:35,500 --> 00:15:36,004

591
00:15:38,059 --> 00:15:38,266

592
00:15:38,381 --> 00:15:38,605

593
00:15:39,720 --> 00:15:40,105

594
00:15:40,431 --> 00:15:41,718

595
00:15:43,763 --> 00:15:44,185

596
00:15:44,912 --> 00:15:48,557
ดูตดนี้นะคะกำหนดให้

597
00:15:48,951 --> 00:15:49,240

598
00:15:49,140 --> 00:15:49,422

599
00:15:49,330 --> 00:15:49,556

600
00:15:49,460 --> 00:15:49,941

601
00:15:50,030 --> 00:15:50,315

602
00:15:50,867 --> 00:15:51,447

603
00:15:52,861 --> 00:15:55,405
ลำดับของ

604
00:15:56,379 --> 00:15:58,358
13

605
00:15:59,140 --> 00:15:59,764

606
00:16:00,160 --> 00:16:00,549

607
00:16:00,799 --> 00:16:01,086

608
00:16:00,997 --> 00:16:01,211

609
00:16:01,190 --> 00:16:01,889

610
00:16:01,828 --> 00:16:02,096

611
00:16:02,078 --> 00:16:03,501
จุดจุดจุด

612
00:16:03,490 --> 00:16:03,864

613
00:16:03,679 --> 00:16:04,507

614
00:16:04,579 --> 00:16:08,040
กำหนดให้ลำดับของ 1 3 5 7 9

615
00:16:08,360 --> 00:16:08,648

616
00:16:09,071 --> 00:16:10,244
อนุกรม

617
00:16:10,152 --> 00:16:10,392

618
00:16:10,601 --> 00:16:10,851

619
00:16:11,950 --> 00:16:14,867
ข้อนี้มีค่าเท่าใด

620
00:16:17,708 --> 00:16:20,836
ใครจะลองคะ

621
00:16:21,108 --> 00:16:22,885
หา sn ข้อนี้

622
00:16:22,900 --> 00:16:23,161

623
00:16:23,600 --> 00:16:24,055

624
00:16:24,058 --> 00:16:24,449

625
00:16:25,083 --> 00:16:25,971

626
00:16:26,110 --> 00:16:29,423
โอเคเชิญค่ะ

627
00:16:30,331 --> 00:16:30,831

628
00:16:30,968 --> 00:16:32,246

629
00:16:32,449 --> 00:16:32,895

630
00:16:32,900 --> 00:16:33,270

631
00:16:33,218 --> 00:16:33,447

632
00:16:33,349 --> 00:16:34,616

633
00:16:38,660 --> 00:16:39,003

634
00:16:39,361 --> 00:16:39,602

635
00:16:51,728 --> 00:16:51,964

636
00:16:53,391 --> 00:16:53,869

637
00:17:03,001 --> 00:17:03,292

638
00:17:03,257 --> 00:17:03,499

639
00:17:03,509 --> 00:17:07,745
อารมณ์รูปที่นั่งดูเพื่อนนะคะคิดตามเพื่อนไปด้วยนะ

640
00:17:08,069 --> 00:17:09,470
ตามไปด้วยนะคะ

641
00:17:11,330 --> 00:17:11,952

642
00:17:12,098 --> 00:17:12,410

643
00:17:12,685 --> 00:17:17,419
สามารถหาค่าของอนุกรมรอเพื่อนได้เลยนะคะเรามาดูว่า

644
00:17:17,868 --> 00:17:19,796
คำตอบเราจะตรงกับเพื่อนไหม

645
00:17:20,681 --> 00:17:20,888

646
00:17:22,287 --> 00:17:22,497

647
00:17:22,548 --> 00:17:22,783

648
00:17:23,194 --> 00:17:23,443

649
00:17:23,567 --> 00:17:24,006

650
00:17:24,717 --> 00:17:25,273

651
00:17:25,487 --> 00:17:26,174

652
00:17:26,448 --> 00:17:26,674

653
00:17:27,280 --> 00:17:29,471
ลำดับนี้มีกี่พจน์คะ

654
00:17:29,528 --> 00:17:29,809

655
00:17:29,979 --> 00:17:31,843
มาช่วยกันตอบซิ

656
00:17:31,829 --> 00:17:32,248

657
00:17:32,994 --> 00:17:34,130
เลย

658
00:17:36,189 --> 00:17:36,456

659
00:17:36,569 --> 00:17:37,019

660
00:17:36,827 --> 00:17:37,118

661
00:17:37,540 --> 00:17:37,792

662
00:17:37,925 --> 00:17:38,967
พี่พจน์คะ

663
00:17:39,008 --> 00:17:39,239

664
00:17:39,967 --> 00:17:40,236

665
00:17:40,288 --> 00:17:43,403
ระดับนี้มีกี่พจน์ 1 3 5 7 9

666
00:17:43,938 --> 00:17:45,915
bnk ตัว

667
00:17:45,928 --> 00:17:47,980
bnk ตัว

668
00:17:48,939 --> 00:17:49,246

669
00:17:50,276 --> 00:17:50,533

670
00:17:51,239 --> 00:17:51,485

671
00:17:51,498 --> 00:17:51,992

672
00:17:52,069 --> 00:17:52,310

673
00:17:52,456 --> 00:17:53,348

674
00:17:53,550 --> 00:17:53,908

675
00:17:53,869 --> 00:17:54,143

676
00:17:54,127 --> 00:17:55,931
พูดได้พูดได้ออกเสียงได้

677
00:17:56,628 --> 00:17:57,579

678
00:17:57,705 --> 00:17:59,690
อนุกรมมีกี่พจน์

679
00:17:59,630 --> 00:18:01,672
5:00 น

680
00:18:01,869 --> 00:18:02,823

681
00:18:03,669 --> 00:18:07,550
อนุกรมนี้มีทั้งหมด 5 โพสต์ถูกไหมคะ

682
00:18:07,386 --> 00:18:10,403
งั้นถ้าเราจะหาอนุกรมมีค่าเท่าใด

683
00:18:10,337 --> 00:18:11,487
เราก็แทน

684
00:18:11,748 --> 00:18:12,857
sn

685
00:18:12,899 --> 00:18:14,262
เท่ากับ A1

686
00:18:14,433 --> 00:18:18,342
1 + 12 + 13 + 14 + 15

687
00:18:18,267 --> 00:18:19,081
ไม่รู้

688
00:18:19,367 --> 00:18:23,521
มาแทนค่าเลยไปขึ้น 1 + 3 + 5 +

689
00:18:23,396 --> 00:18:23,839

690
00:18:23,846 --> 00:18:24,947
หมวกลาว

691
00:18:25,069 --> 00:18:25,695

692
00:18:25,708 --> 00:18:28,255

693
00:18:28,658 --> 00:18:31,797
เท่าไหร่คะเนี่ยเพื่อนหาได้ 25 ตรงไหม

694
00:18:31,726 --> 00:18:32,884
ส่งเราไหมคะ

695
00:18:33,968 --> 00:18:35,938
บวกแล้วได้ 25 ไหมลูก

696
00:18:37,557 --> 00:18:38,135

697
00:18:38,141 --> 00:18:39,086
15 ไหม

698
00:18:39,099 --> 00:18:39,409

699
00:18:39,476 --> 00:18:39,853

700
00:18:40,756 --> 00:18:45,534
25 ถูกต้องนะคะ 1 + 3 เป็น 4 4 + 5 เป็น

701
00:18:45,825 --> 00:18:48,181
99 + 7%

702
00:18:48,188 --> 00:18:49,395
16

703
00:18:49,406 --> 00:18:51,131
และ 16 + 9

704
00:18:51,267 --> 00:18:52,048
อากาศ

705
00:18:52,037 --> 00:18:55,690
25 ข้อนี้นะคะอนุกรมมีค่า

706
00:18:55,749 --> 00:18:58,615
25 นั้น AR เก่งมากเลยเพื่อนหน่อย

707
00:18:58,567 --> 00:19:00,753

708
00:19:00,686 --> 00:19:02,815
ราคาเข่งมากับรถ

709
00:19:02,747 --> 00:19:03,041

710
00:19:03,116 --> 00:19:03,368

711
00:19:03,379 --> 00:19:03,662

712
00:19:03,565 --> 00:19:05,789

713
00:19:07,796 --> 00:19:08,016

714
00:19:08,115 --> 00:19:11,508
โอเคมาดูข้อต่อไปนะคะ

715
00:19:11,516 --> 00:19:11,758

716
00:19:12,409 --> 00:19:12,906

717
00:19:12,858 --> 00:19:14,632

718
00:19:17,597 --> 00:19:17,801

719
00:19:17,858 --> 00:19:18,546

720
00:19:18,626 --> 00:19:18,855

721
00:19:32,975 --> 00:19:36,518
มาดูตัวอย่างต่อไป

722
00:19:36,427 --> 00:19:39,637
มาดูว่าใครจะออกมาหาคำตอบไม่ได้บ้างนะคะ

723
00:19:42,586 --> 00:19:44,454
คิดนะคิดตามนะ

724
00:19:44,701 --> 00:19:44,984

725
00:19:44,886 --> 00:19:45,098

726
00:19:45,786 --> 00:19:46,035

727
00:19:46,808 --> 00:19:47,037

728
00:19:47,634 --> 00:19:47,910

729
00:19:47,827 --> 00:19:48,076

730
00:19:48,029 --> 00:19:48,324

731
00:19:48,278 --> 00:19:48,665

732
00:19:48,665 --> 00:19:48,919

733
00:19:48,927 --> 00:19:49,215

734
00:19:50,660 --> 00:19:50,935

735
00:19:51,107 --> 00:19:51,607

736
00:19:51,808 --> 00:19:52,059

737
00:19:54,366 --> 00:19:54,793

738
00:19:55,065 --> 00:19:55,960

739
00:19:58,915 --> 00:19:59,136

740
00:20:29,739 --> 00:20:30,004

741
00:20:33,069 --> 00:20:33,288

742
00:20:37,028 --> 00:20:40,303

743
00:20:40,234 --> 00:20:40,670

744
00:20:42,028 --> 00:20:45,557
อาทิตย์นี้มาดูตัวอย่างต่อไปนะคะ

745
00:20:45,547 --> 00:20:45,786

746
00:20:45,746 --> 00:20:48,312
วันนี้จะมีความซับซ้อนขึ้นมานิดนึง

747
00:20:48,309 --> 00:20:48,598

748
00:20:48,826 --> 00:20:49,901
นิดนึงเนาะ

749
00:20:50,037 --> 00:20:50,606

750
00:20:51,258 --> 00:20:51,532

751
00:20:52,025 --> 00:20:56,375
โจทย์บอกว่าจงหาผลบวกของ 5 พจน์แรกของลำดับ

752
00:20:56,267 --> 00:20:56,556

753
00:20:56,415 --> 00:20:58,050
135

754
00:20:58,116 --> 00:20:58,555

755
00:20:58,506 --> 00:20:58,815

756
00:20:58,825 --> 00:20:59,196

757
00:20:59,274 --> 00:20:59,649

758
00:21:00,675 --> 00:21:04,468
เรารู้แล้วว่าอนุกรมก็คือผลบวกของลำดับถูกไหมคะ

759
00:21:04,595 --> 00:21:05,478
ใช่ไหม

760
00:21:05,617 --> 00:21:07,393
อนุกรมคือผลบวกของลำดับ

761
00:21:07,474 --> 00:21:11,269
แต่โจทย์ข้อนี้เขาบอกลำดับมาแค่

762
00:21:11,197 --> 00:21:12,717
135

763
00:21:12,854 --> 00:21:13,754
แค่กี่

764
00:21:13,816 --> 00:21:14,839
ตัวคะ

765
00:21:15,417 --> 00:21:21,035
มีแค่ 3 ตัวแต่โจทย์เค้าให้เราหา 5 พจน์แรก

766
00:21:21,377 --> 00:21:21,687

767
00:21:21,826 --> 00:21:22,069

768
00:21:22,145 --> 00:21:22,516

769
00:21:22,784 --> 00:21:23,743

770
00:21:23,746 --> 00:21:28,795
อยากไปไหมนี่ฮ่าๆๆแสดงว่าโจทก์ยังไม่ครบถูกไหมคะลูก

771
00:21:29,707 --> 00:21:32,067
เขาให้หาห้าพจน์แรก

772
00:21:32,006 --> 00:21:34,269
โจทย์ให้มาแค่ 3 หัว

773
00:21:35,914 --> 00:21:40,495
ชายแดนข้อนี้เราจะต้องเป็นไงคะหา

774
00:21:40,654 --> 00:21:42,734
เพิ่มอีก 2 คนถูกไหมคะ

775
00:21:42,704 --> 00:21:43,120

776
00:21:43,022 --> 00:21:47,185
งั้นเราก็จะได้ย้อนกลับไปความรู้เดิมที่เราเรียนผ่านมาแล้ว

777
00:21:47,253 --> 00:21:48,967
คือเรื่องของลำดับ

778
00:21:49,945 --> 00:21:51,023

779
00:21:51,285 --> 00:21:53,011
เรื่องของการหาพท

780
00:21:53,599 --> 00:22:00,347
การหาพจน์แรกสามพจน์แรก 4/1 พจน์ที่ N ของลำดับจำได้ไหมมันจะมีสูตรในการหา

781
00:22:00,263 --> 00:22:01,078

782
00:22:01,355 --> 00:22:02,485
โดยใช้สูตร

783
00:22:02,565 --> 00:22:03,561

784
00:22:03,527 --> 00:22:03,935

785
00:22:03,657 --> 00:22:05,016
เท่ากับ A1

786
00:22:05,123 --> 00:22:07,870
บวกในวงเล็บ n - 1

787
00:22:08,848 --> 00:22:10,399
วงเล็บคุณได้ดี

788
00:22:11,276 --> 00:22:13,631
อันนี้คือสูตรการหาอะไรคะ

789
00:22:13,775 --> 00:22:15,635
หาพจน์ที่ n ถูกไหมคะ

790
00:22:16,274 --> 00:22:19,580
ย้อนความรู้นิดนึงถือว่าเป็นการทบทวนเนาะ

791
00:22:19,544 --> 00:22:21,406
งั้นแค่นี้นะคะ

792
00:22:21,333 --> 00:22:21,718

793
00:22:21,655 --> 00:22:21,946

794
00:22:21,912 --> 00:22:24,309
เราจะต้องรู้ว่า A 1 คืออะไร

795
00:22:24,405 --> 00:22:26,290
ใครทราบ a10 เลขอะไรคะ

796
00:22:27,238 --> 00:22:28,432
ไม่ตอบเลยค่ะ

797
00:22:28,636 --> 00:22:29,016

798
00:22:29,854 --> 00:22:31,577
A1 คือ

799
00:22:31,772 --> 00:22:32,168

800
00:22:32,094 --> 00:22:33,879
ซื้อเลขอะไรคะ

801
00:22:35,623 --> 00:22:42,045
คนนี้ยกมือคนนี้ตอบอย่างมากคือ 1 นะคะถูกต้องค่ะยำมา

802
00:22:41,966 --> 00:22:44,341
a101 นะคะ

803
00:22:44,653 --> 00:22:47,384
สูตรมันต้องหาค่าดีด้วย

804
00:22:47,665 --> 00:22:49,724
ไม่มีคดีคืออะไร

805
00:22:49,713 --> 00:22:50,108

806
00:22:50,104 --> 00:22:50,531

807
00:22:50,483 --> 00:22:53,372
มันมีเฉลยแล้วอ่ะอย่าเพิ่งดูสิ

808
00:22:53,626 --> 00:22:53,917

809
00:22:53,812 --> 00:22:54,891

810
00:22:55,415 --> 00:22:58,909
ข้อดีคืออะไรคะผลต่างร่วมใช่ไหม

811
00:22:58,813 --> 00:22:59,436

812
00:22:59,453 --> 00:23:02,144
ค่า D คือผลต่างร่วม

813
00:23:02,013 --> 00:23:02,566

814
00:23:02,525 --> 00:23:07,931
ทางคุณเจนก่อนผู้เรียนถามว่าค่า D คือผลต่างร่วมใช่ไหม

815
00:23:08,108 --> 00:23:10,277
ซึ่งเราสามารถหาคดีได้

816
00:23:10,593 --> 00:23:11,557
ว่ายังไงคะ

817
00:23:13,413 --> 00:23:14,307
การนำ

818
00:23:14,636 --> 00:23:14,893

819
00:23:15,213 --> 00:23:21,188
พจน์ที่อยู่ใกล้ๆกันมา 1 คู่ใช่ไหมแล้วนำพจน์ข้างหลัง - พุธข้างหน้าใช่ไหมคะ

820
00:23:21,166 --> 00:23:24,875
ยังข้อนี้เราอาจจะเอาคู่ 1 และ 3 มา

821
00:23:25,073 --> 00:23:27,855
แล้วก็เอา 3 - ออก 1

822
00:23:28,217 --> 00:23:29,031

823
00:23:29,173 --> 00:23:30,325
จะได้ 2

824
00:23:30,465 --> 00:23:30,689

825
00:23:30,593 --> 00:23:35,922
งั้นแค่นี้เราก็สรุปได้ว่าตีของอนุกรมนี้คือใช่

826
00:23:35,833 --> 00:23:39,442
ต้องเข้าใจด้วยนะว่า 2 มาจากเอาอะไรคะ

827
00:23:39,552 --> 00:23:42,601
ครุฑหลัง - หน้าคือเอา 3 - 1 ได้

828
00:23:43,278 --> 00:23:44,286
2

829
00:23:44,296 --> 00:23:46,550
แล้วถ้าเอา 5 - 3 ก็ได้

830
00:23:47,503 --> 00:23:48,833
2 เหมือนกัน

831
00:23:48,974 --> 00:23:52,173
มันเอาศพในบ้านดีของข้อนี้มีค่าเท่ากับ

832
00:23:52,431 --> 00:23:53,297
รู้แล้ว

833
00:23:53,194 --> 00:23:53,452

834
00:23:53,455 --> 00:23:55,169
A1 น่ะคืนนึง

835
00:23:54,991 --> 00:23:55,249

836
00:23:55,124 --> 00:23:56,387
รู้ดีแล้วคือ

837
00:23:56,532 --> 00:24:01,977
เรานำมาแทนค่าในในสูตรของเราได้เลยเพื่อที่จะหา

838
00:24:01,843 --> 00:24:02,820
พจน์ที่ n

839
00:24:03,391 --> 00:24:05,868
ที่มันยังไม่ครบในโจทย์ถูกไหมคะ

840
00:24:06,335 --> 00:24:06,601

841
00:24:06,593 --> 00:24:06,902

842
00:24:08,122 --> 00:24:10,480
วุฒิยังไม่ทราบคือพจน์ที่เท่าไหร่คะ

843
00:24:11,142 --> 00:24:16,780
คือบทที่ 4 และพจน์ที่ 5 2 คนใช่ไหมคะเพราะพุธที่ 1

844
00:24:16,964 --> 00:24:18,349
ให้มาแล้วคืนนึง

845
00:24:18,565 --> 00:24:21,165
บทที่ 2 จดให้มาแล้วคือ

846
00:24:21,133 --> 00:24:22,094
3

847
00:24:22,093 --> 00:24:22,375

848
00:24:22,222 --> 00:24:24,306
และพจน์ที่ 3 จดให้มาแล้วคือ

849
00:24:24,332 --> 00:24:25,219

850
00:24:25,422 --> 00:24:25,694

851
00:24:26,122 --> 00:24:30,035
แต่ยังไม่ทราบคือพจน์ที่ 4 และพจน์ที่

852
00:24:30,802 --> 00:24:31,427

853
00:24:31,702 --> 00:24:32,132

854
00:24:32,152 --> 00:24:34,901
เราก็สามารถหาได้เลยค่ะโดยการนำ

855
00:24:35,032 --> 00:24:36,015

856
00:24:37,661 --> 00:24:37,921

857
00:24:38,173 --> 00:24:39,931
สูตรนี้มา

858
00:24:40,924 --> 00:24:41,202

859
00:24:41,111 --> 00:24:45,341
นี่มาดูเขาว่าถ้าเราแทนค่า A 1 = 1

860
00:24:45,792 --> 00:24:48,617
บวก n n คือพจน์ที่เรา

861
00:24:48,806 --> 00:24:52,482
ไม่ทราบไหมคะเราไม่ทราบว่าติดเอ็นไว้

862
00:24:52,592 --> 00:24:52,905

863
00:24:52,842 --> 00:24:57,873
ลบหนึ่งแล้วก็คูณด้วยดีๆคือ 22 เข้าไปคุณใช่ไหม

864
00:24:58,044 --> 00:25:01,398
2 คันนึงได้จะได้เป็น 2 n

865
00:25:01,233 --> 00:25:02,520
และ -2

866
00:25:03,282 --> 00:25:05,497
ดูตามนะดูตามนะคะ

867
00:25:05,712 --> 00:25:07,013
เข้าใจนะ

868
00:25:07,120 --> 00:25:11,507
สายตานะมึงนะเราก็จะได้ a n = อะไรคะ

869
00:25:11,481 --> 00:25:13,129
2 n - 1

870
00:25:13,792 --> 00:25:14,976
งงตรงนี้

871
00:25:14,872 --> 00:25:16,372
2 in 1

872
00:25:16,746 --> 00:25:16,999

873
00:25:16,930 --> 00:25:19,114
นักรบ 2 ตัวนี้มีไหม

874
00:25:19,044 --> 00:25:19,282

875
00:25:19,232 --> 00:25:20,318
1 ตรงเนี้ย

876
00:25:20,451 --> 00:25:22,910
มันเป็นจำนวนเต็มเหมือนกันใช่ไหมคะ

877
00:25:23,200 --> 00:25:25,650
มันไม่ติดตัวแปรใดๆเลยเรานำมา

878
00:25:25,831 --> 00:25:26,105

879
00:25:26,224 --> 00:25:27,634
บวกมาลบกันได้เลย

880
00:25:28,330 --> 00:25:29,143

881
00:25:29,291 --> 00:25:29,515

882
00:25:29,481 --> 00:25:31,997
ตามความจริงนะ 1 - 2 ได้ไหม

883
00:25:32,622 --> 00:25:32,845

884
00:25:33,072 --> 00:25:37,598
ไม่ได้ถ้าแบบนี้นะคะเวลาเรานำมาลดเรายังไม่ต้องดูเครื่องหมาย

885
00:25:38,269 --> 00:25:43,686
เรานำตัวเลขที่มากกว่าลบออกเลยเป็น 2 - 1 ใช่ไหมคะ

886
00:25:44,354 --> 00:25:47,143
เป็น 2 - 1 ไหมคะ

887
00:25:47,101 --> 00:25:47,866

888
00:25:47,872 --> 00:25:49,959
ติดเครื่องหมายอะไรดูซิว่า

889
00:25:51,012 --> 00:25:53,949
ตัวที่มีค่ามากมันติดเครื่องหมายอะไร

890
00:25:53,832 --> 00:25:56,588
ยังข้อนี้ 2 มีค่ามากกว่า 1 ถุงไหมลูก

891
00:25:56,770 --> 00:25:59,230
ใช่ไหม 2 มีค่ามากกว่า 1 ใช่ไหม

892
00:26:00,114 --> 00:26:04,002
ชายและหน้าเลข 2 เป็นเครื่องหมายอะไร

893
00:26:04,462 --> 00:26:06,379
เครื่องหมายลบ

894
00:26:06,449 --> 00:26:09,097
คำตอบที่ได้ก็เลยต้องติดลบด้วย

895
00:26:09,910 --> 00:26:12,292
2 - 1 เท่ากับ 1 นะถูกแล้ว

896
00:26:12,210 --> 00:26:12,553

897
00:26:12,724 --> 00:26:14,117
ต้องติดเครื่องหมายลบ

898
00:26:14,074 --> 00:26:14,564

899
00:26:14,846 --> 00:26:17,923
ชายชาย

900
00:26:18,431 --> 00:26:21,508
หน้าเลข 2 เป็นเครื่องหมายลบนั่นเอง

901
00:26:21,430 --> 00:26:21,812

902
00:26:22,072 --> 00:26:24,443
เราได้มาแล้วค่ะอันนี้เป็นอะไรคะ

903
00:26:25,223 --> 00:26:25,503

904
00:26:25,790 --> 00:26:29,630
พจน์ทั่วไปถูกไหมพจน์ทั่วไปที่เราจะนำมาหา

905
00:26:30,021 --> 00:26:33,713
พจน์ที่ 4 และพจน์ที่ 5 ที่เราต้องการทราบถูกไหมคะ

906
00:26:34,570 --> 00:26:38,682
โอเคนะตามไม่ทันนะไอ้ตามไม่ทันบอกนะลูก

907
00:26:38,871 --> 00:26:39,186

908
00:26:39,701 --> 00:26:41,363
นึกว่าเจนให้ค่ารถเมล์

909
00:26:41,432 --> 00:26:42,498

910
00:26:42,769 --> 00:26:45,320
ขึ้นรถเมล์ตามไม่ทัน

911
00:26:45,970 --> 00:26:49,096
มาถึงตรงนี้เราก็สามารถหาพจน์ที่ 4 ได้เลย

912
00:26:49,430 --> 00:26:50,907
โดยแทนค่า

913
00:26:51,231 --> 00:26:54,408
KN ก็เป็น A4

914
00:26:54,681 --> 00:26:56,156
แผ่น NS =

915
00:26:56,029 --> 00:26:57,446
เลข 4 ไปเลย

916
00:26:57,570 --> 00:26:59,229
ชายค่ะ

917
00:26:59,749 --> 00:27:02,865
A4 ก็จะกลับไงก็ 2 x

918
00:27:03,661 --> 00:27:08,320
n คือเลข 4 ใช่ไหมคือ 2 * 4 เลยใช่แล้วลบด้วย

919
00:27:09,421 --> 00:27:12,078
มันก็จะเป็นการบวกลบเลขธรรมดาแล้วทีนี้

920
00:27:11,730 --> 00:27:11,975

921
00:27:11,991 --> 00:27:12,304

922
00:27:12,241 --> 00:27:14,104
2 * 4 เท่าไหร่คะ

923
00:27:14,422 --> 00:27:14,690

924
00:27:14,609 --> 00:27:15,829
2 * 4

925
00:27:16,403 --> 00:27:19,382
ซ้อมไว้ซ้อมไว้ใครจะไปแข่งคณิตศาสตร์ซ้อมไว้นะคะ

926
00:27:19,471 --> 00:27:20,819
2 * 4

927
00:27:21,151 --> 00:27:26,069
แป๊บนึงมากค่ะ 2 + 4 = 8 - ออก 1

928
00:27:26,332 --> 00:27:26,720

929
00:27:26,650 --> 00:27:27,014

930
00:27:27,159 --> 00:27:32,115
7 ซองบทที่ 4 ตรงนี้ได้แล้วคือเลข

931
00:27:32,104 --> 00:27:32,792
เจ็บ

932
00:27:33,831 --> 00:27:34,127

933
00:27:34,081 --> 00:27:35,415
ยังไม่จบนะ

934
00:27:35,431 --> 00:27:38,377
เพราะเขาบอกว่าต้องเป็น 5 พจน์แรก

935
00:27:38,762 --> 00:27:40,390
เราก็ต้องหาคนที่ 5

936
00:27:41,450 --> 00:27:45,514
ตี 5 แผ่น A5 ไปเลยใช่ไหมคะ

937
00:27:45,680 --> 00:27:46,640
เท่ากับ

938
00:27:46,829 --> 00:27:47,854
2

939
00:27:48,179 --> 00:27:49,266
x n

940
00:27:49,649 --> 00:27:51,983
เลข 5 แผงครับ

941
00:27:51,380 --> 00:27:56,247
2 * 5 = กาย 10 เก่งมาค่ะรอแป๊บนึง

942
00:27:56,632 --> 00:27:57,008

943
00:27:57,079 --> 00:27:58,559
ศิลปะป 1

944
00:27:58,679 --> 00:28:05,231
9 เก่งมากไม่น่ารักได้ยินเสียงด้วยนั่นคือ

945
00:28:05,286 --> 00:28:06,701
บทที่ 5 เท่ากับ

946
00:28:07,009 --> 00:28:07,301

947
00:28:07,139 --> 00:28:07,895

948
00:28:08,553 --> 00:28:12,671
ได้ครบแล้วนะพูดแล้วนะตามที่โจทย์ต้องการทราบแล้ว

949
00:28:13,550 --> 00:28:16,286
เราก็มาเขียนนะคะ 5 พจน์แรก

950
00:28:16,620 --> 00:28:16,903

951
00:28:16,809 --> 00:28:20,826
ก็คือ 135 ที่จดให้มา

952
00:28:20,981 --> 00:28:21,872
ใช่ไหม

953
00:28:22,001 --> 00:28:24,246
และเห็ดที่เราหาได้

954
00:28:24,368 --> 00:28:24,942

955
00:28:24,949 --> 00:28:26,665
ได้เพิ่มขึ้นมา

956
00:28:27,131 --> 00:28:28,485
5 คนหรือยัง

957
00:28:29,239 --> 00:28:30,072

958
00:28:31,029 --> 00:28:36,229
1 2 3 4 5 ครบทั้ง 5 พจน์แล้วเราก็มาเขียน

959
00:28:37,309 --> 00:28:39,675
ในรูปผลบวกของลำดับ

960
00:28:39,809 --> 00:28:41,535
นั่นคือเราจะหาอนุกรมกันและ

961
00:28:42,120 --> 00:28:45,004
sn หรือ S5 ใช่ไหมคะ

962
00:28:45,190 --> 00:28:46,523
ตามโจทย์

963
00:28:47,239 --> 00:28:47,548

964
00:28:47,428 --> 00:28:50,110
F5 ก็เท่ากับ 1 +

965
00:28:50,321 --> 00:28:52,048
3 +

966
00:28:51,988 --> 00:28:53,193
5 +

967
00:28:53,205 --> 00:28:54,852
7 + 9

968
00:28:55,439 --> 00:28:56,328
เอากลับ

969
00:28:56,659 --> 00:29:01,638
25 วันนั้นนะครับผลบวกของ 5 พจน์แรกของ

970
00:29:01,589 --> 00:29:03,891
135

971
00:29:04,282 --> 00:29:05,576
ก็คือเท่าไหร่คะ

972
00:29:05,631 --> 00:29:07,288
25 นั่นเอง

973
00:29:08,509 --> 00:29:08,895

974
00:29:09,031 --> 00:29:09,336

975
00:29:09,281 --> 00:29:09,777

976
00:29:09,789 --> 00:29:15,103
จะถามอะไรไหมคะเข้าใจไหมเข้าใจถ้าเข้าใจต้องทำตัวอย่างได้นะ

977
00:29:14,989 --> 00:29:16,582
เดี๋ยวดูต่อไป

978
00:29:17,161 --> 00:29:17,899

979
00:29:17,988 --> 00:29:18,358

980
00:29:18,568 --> 00:29:18,997

981
00:29:20,548 --> 00:29:23,095
เมื่อกี้เป็นวิธีแรก

982
00:29:23,309 --> 00:29:23,543

983
00:29:23,759 --> 00:29:24,191

984
00:29:24,149 --> 00:29:27,374
เป็นวิธีหนึ่งที่ในที่ใช้ในการหาอนุกรม

985
00:29:27,728 --> 00:29:29,450
มันมีอีกวิธีนึงลูก

986
00:29:29,709 --> 00:29:31,577
ที่ง่ายกว่าวิธีเมื่อกี้

987
00:29:32,150 --> 00:29:32,573

988
00:29:32,408 --> 00:29:34,059
ได้คำตอบเหมือนกัน

989
00:29:35,477 --> 00:29:38,840
มาดูนะวิธีนี้คืออะไรกันค่ะ

990
00:29:38,810 --> 00:29:39,177

991
00:29:39,270 --> 00:29:40,154
จงหา

992
00:29:40,229 --> 00:29:43,378
ผลบวกของ 5 พจน์แรกของลำดับ 135

993
00:29:43,301 --> 00:29:44,513

994
00:29:45,028 --> 00:29:45,585

995
00:29:45,600 --> 00:29:45,812

996
00:29:46,368 --> 00:29:51,574
วิธีนี้เขาบอกว่าแค่เราสามารถหาผลต่างร่วม

997
00:29:52,009 --> 00:29:53,788
หรือหาค่าดี

998
00:29:54,380 --> 00:29:56,246
ไม่ได้

999
00:29:56,818 --> 00:29:58,984
เราก็สามารถหาผลบวกได้เลย

1000
00:29:59,380 --> 00:30:02,104
อนุกรมได้เลยมาดูว่าเป็นยังไง

1001
00:30:02,320 --> 00:30:03,488
ดูหนัง

1002
00:30:04,119 --> 00:30:04,392

1003
00:30:04,510 --> 00:30:05,916
หาค่า D

1004
00:30:07,448 --> 00:30:08,338

1005
00:30:08,989 --> 00:30:12,097
ถ้าดีหาได้จากอะไรนะ

1006
00:30:11,997 --> 00:30:14,251
คดีหาได้จ้า

1007
00:30:14,690 --> 00:30:18,179
นำพดหลัง - หน้าใช่ไหมคะ

1008
00:30:18,340 --> 00:30:20,157
เอาคนที่อยู่ใกล้กันนะลูก

1009
00:30:20,328 --> 00:30:21,408
มา 1 คู่

1010
00:30:21,607 --> 00:30:24,372
แล้วนำตัวเลขที่อยู่ข้างหลังลบตัวเลขที่อยู่ข้างหน้า

1011
00:30:24,548 --> 00:30:27,505
วันนี้เอาคู่ 13 มา

1012
00:30:27,371 --> 00:30:28,826
1 กับ 3

1013
00:30:29,358 --> 00:30:33,390
ตามอยู่ข้างหลังใช่ไหมเอา 3 - ตัวข้างหน้าคือเลข 1

1014
00:30:33,652 --> 00:30:34,924
เราก็จะได้คำตอบคือ

1015
00:30:35,124 --> 00:30:35,821

1016
00:30:36,207 --> 00:30:36,478

1017
00:30:36,858 --> 00:30:40,319
ลองพิสูจน์ดูว่าใช่หรือไม่ว่า 3 - 1 = 2

1018
00:30:40,249 --> 00:30:43,617
จริงและ 5 - 3 เท่ากับ 2 ไหม

1019
00:30:44,669 --> 00:30:46,424
ลบออก 3 เท่ากับ 2 ไหม

1020
00:30:46,980 --> 00:30:47,787

1021
00:30:47,748 --> 00:30:48,515
ลบออก

1022
00:30:48,708 --> 00:30:49,326

1023
00:30:49,858 --> 00:30:51,092
เท่ากับ 2 ไหม

1024
00:30:51,067 --> 00:30:54,260
เอาไหมเอาไหม

1025
00:30:54,537 --> 00:30:55,804
เอาใช่ไหมคะ

1026
00:30:55,878 --> 00:30:59,429
ถ้าเท่ากันไปเรื่อยๆแบบนี้ก็แสดงว่าดีเท่ากับ 2

1027
00:30:59,718 --> 00:31:00,028

1028
00:31:00,109 --> 00:31:04,513
พอทราบค่าดีนะคะเขาบอกว่าให้พิจารณาเลยค่ะว่า

1029
00:31:04,720 --> 00:31:08,273
พจน์ที่ 1 ไปพจน์ที่ 2 ห่างกัน 2 ใช่ไหม

1030
00:31:08,747 --> 00:31:12,208
ห่างกัน 2 ก็คือบวกเพิ่ม 1 บวกเพิ่มอีก 2

1031
00:31:12,147 --> 00:31:13,448
เท่ากับพจน์ที่ 2

1032
00:31:13,947 --> 00:31:15,026
ใช่หรือไม่

1033
00:31:14,971 --> 00:31:15,589

1034
00:31:15,737 --> 00:31:16,256

1035
00:31:16,249 --> 00:31:19,837
อาวุธที่ 2 บวกเพิ่มอีก 2 เท่ากับคนที่ 3 ใช่หรือไม่

1036
00:31:20,801 --> 00:31:25,172
จากนั้นเอาพุธที่ 3 บวกเพิ่มอีก 2 มันจะเข้ากับคนที่

1037
00:31:25,149 --> 00:31:25,722

1038
00:31:26,507 --> 00:31:31,034
และพุธที่ 4 บวกเพิ่มอีก 2 มันจะเท่ากับ 5 ไปแบบนี้เรื่อยๆ

1039
00:31:33,867 --> 00:31:37,919
แบบนี้เราก็จะสามารถหาพจน์ต่อไปได้ไม่ยากเลย

1040
00:31:38,348 --> 00:31:40,464
มาดูพิสูจน์กันซิ

1041
00:31:40,466 --> 00:31:41,597
1

1042
00:31:41,747 --> 00:31:43,743
หมวก DD คือ 2

1043
00:31:43,738 --> 00:31:45,121
เท่ากับ 3 ไหมคะ

1044
00:31:45,717 --> 00:31:46,010

1045
00:31:46,168 --> 00:31:47,704
1

1046
00:31:47,708 --> 00:31:48,465

1047
00:31:48,409 --> 00:31:49,220
2

1048
00:31:49,237 --> 00:31:49,541

1049
00:31:49,558 --> 00:31:51,416
เท่ากับ 3 ไหม

1050
00:31:51,617 --> 00:31:52,515
เอาไหม

1051
00:31:53,347 --> 00:31:54,937
ไหนว่าไม่เท่า

1052
00:31:54,817 --> 00:31:55,048

1053
00:31:55,022 --> 00:31:59,594
เอาเท่าน้องแล้ว 3 + 2 ล่ะ

1054
00:32:00,071 --> 00:32:01,301
เท่ากับ 5 ไหม

1055
00:32:02,190 --> 00:32:04,746
3 + 2

1056
00:32:04,939 --> 00:32:05,249

1057
00:32:05,188 --> 00:32:10,984
เท่ากับ 5 ไหมเท่ากับ 55 ชายแต่นั้นมาดูเขาอ่ะ

1058
00:32:11,087 --> 00:32:12,622
5 + 2 ค่ะ

1059
00:32:13,199 --> 00:32:13,588

1060
00:32:13,588 --> 00:32:15,547
เอา 5 + 2 ค่ะ

1061
00:32:15,449 --> 00:32:16,522
เป็นเท่าไหร่คะ

1062
00:32:16,668 --> 00:32:17,672

1063
00:32:18,906 --> 00:32:22,731
หนูแค่ 7แสนวอนลำดับต่อไปคือ 7 ละ

1064
00:32:22,749 --> 00:32:27,318
ฉันเอา 7 + 2 ค่ะ

1065
00:32:27,747 --> 00:32:32,354
ลำดับต่อไปคือเลข 9 แบบนี้เราสามารถหาลำดับถัดไปเรื่อยๆนะคะ

1066
00:32:32,678 --> 00:32:33,831
ได้ไหม

1067
00:32:35,109 --> 00:32:38,446
เราสามารถหาลำดับถัดไปได้เรื่อยๆไหมคะ

1068
00:32:39,267 --> 00:32:39,978

1069
00:32:39,989 --> 00:32:40,799

1070
00:32:40,746 --> 00:32:43,920
เพราะเรารู้ว่าดีมันมีค่าเท่ากับ 2

1071
00:32:43,889 --> 00:32:44,148

1072
00:32:44,077 --> 00:32:46,408
พูดแล้วมันห่างกันคืออะไรคะ

1073
00:32:46,708 --> 00:32:49,998
มันเพิ่มขึ้นทีละ 2 2 2

1074
00:32:50,356 --> 00:32:53,624
ลำดับถัดไปคือเอา 9+ กับ 2 ถูกไหมคะ

1075
00:32:53,633 --> 00:32:54,303

1076
00:32:54,386 --> 00:32:56,568
9 + 2 เป็นเท่าไหร่

1077
00:32:56,506 --> 00:32:56,929

1078
00:32:57,668 --> 00:32:57,921

1079
00:32:57,986 --> 00:32:58,233

1080
00:32:58,369 --> 00:32:59,185
9

1081
00:32:59,328 --> 00:33:00,793
บวกเพิ่มอีก 2

1082
00:33:00,736 --> 00:33:01,009

1083
00:33:01,187 --> 00:33:01,471

1084
00:33:01,436 --> 00:33:03,545
11 ชาย

1085
00:33:03,549 --> 00:33:05,271
ลำดับถัดไปคือ 11

1086
00:33:05,611 --> 00:33:08,700
ไปอีกเรื่อยๆแล้วก็สมัครหาได้เรื่อยๆ

1087
00:33:08,747 --> 00:33:09,008

1088
00:33:09,186 --> 00:33:12,377
แต่ในโจทย์ข้อนี้เราไม่ต้องหาต่อแล้วค่ะเพราะ

1089
00:33:12,587 --> 00:33:15,732
โจทย์เขาถามแค่ 5 พจน์แรกใช่ไหมคะ

1090
00:33:15,917 --> 00:33:16,298

1091
00:33:16,877 --> 00:33:19,238
ไปนั้นเราก็จะหาได้

1092
00:33:19,116 --> 00:33:24,412
เอาแค่ 5 โพสต์นี้เท่านั้นพอได้ 5 พจน์แล้วเราก็

1093
00:33:24,436 --> 00:33:27,709
มาหาผลบวกของลำดับทั้ง 5

1094
00:33:28,148 --> 00:33:32,027
อนุกรมนั้นเองหาค่าของอนุกรมของลำดับนี้

1095
00:33:32,581 --> 00:33:33,202

1096
00:33:33,149 --> 00:33:34,760
เป็น S5

1097
00:33:35,006 --> 00:33:35,245

1098
00:33:35,197 --> 00:33:36,811
เท่ากับ 1

1099
00:33:37,068 --> 00:33:38,539
+3

1100
00:33:38,538 --> 00:33:41,026
+ 5 + 7 + 9

1101
00:33:41,155 --> 00:33:43,099
ซึ่งคำตอบก็คืออะไรคะ

1102
00:33:43,468 --> 00:33:43,779

1103
00:33:43,788 --> 00:33:45,053
25

1104
00:33:44,997 --> 00:33:45,252

1105
00:33:45,136 --> 00:33:48,348
เท่ากันไหมเท่ากันกับตัวอย่างแรกไหมคะ

1106
00:33:49,302 --> 00:33:51,343
ตัวอย่างที่คำตอบก็คือ

1107
00:33:51,727 --> 00:33:52,991
25

1108
00:33:52,949 --> 00:33:53,242

1109
00:33:53,198 --> 00:33:55,556
ตัวเดียวกันนะ

1110
00:33:56,348 --> 00:33:56,606

1111
00:33:57,048 --> 00:33:59,643
หาด้วยวิธีนี้คำตอบก็

1112
00:33:59,928 --> 00:34:01,007
อะไรนะ

1113
00:34:01,147 --> 00:34:02,757
25 เหมือนกัน

1114
00:34:02,686 --> 00:34:02,967

1115
00:34:03,007 --> 00:34:04,538
คำตอบเดียวกัน

1116
00:34:04,478 --> 00:34:06,331
วิธีการหาค่

1117
00:34:06,466 --> 00:34:07,982
นั่นเอง

1118
00:34:07,996 --> 00:34:11,390
มาถึงตรงนี้ลูกๆคิดว่า

1119
00:34:11,846 --> 00:34:12,122

1120
00:34:12,108 --> 00:34:14,034
ระหว่างวิธีนี้ลูก

1121
00:34:15,496 --> 00:34:17,042
วิธีนี้ลูก

1122
00:34:17,346 --> 00:34:22,997
คือต้องหาพจน์ทั่วไปของลำดับก่อนแล้วค่อยหาคำตอบของอนุกรม

1123
00:34:24,265 --> 00:34:25,153
กลับ

1124
00:34:25,616 --> 00:34:25,913

1125
00:34:25,867 --> 00:34:27,415
วิธีนี้ค่ะลูก

1126
00:34:27,422 --> 00:34:27,852

1127
00:34:27,795 --> 00:34:30,194
หาแค่ค่า d ออกมา

1128
00:34:30,225 --> 00:34:30,506

1129
00:34:30,486 --> 00:34:30,945

1130
00:34:30,745 --> 00:34:31,881
แล้ว

1131
00:34:31,897 --> 00:34:36,210
หาคำตอบของอนุกรมได้เลยวิธีที่ 1

1132
00:34:36,390 --> 00:34:38,946
2 ง่ายกว่ากันคะ

1133
00:34:39,835 --> 00:34:40,125

1134
00:34:40,026 --> 00:34:41,098

1135
00:34:41,055 --> 00:34:44,097
วิธีที่ 1 หรือวิธีที่ 2 ง่ายกว่ากัน

1136
00:34:44,965 --> 00:34:45,793

1137
00:34:47,847 --> 00:34:51,388
แบบไหนหรือว่าหาง่ายกว่ากัน

1138
00:34:51,567 --> 00:34:54,512
1 หรือ 2 เรื่องหรอ

1139
00:34:54,446 --> 00:34:55,477
จริงอ่ะ

1140
00:34:55,786 --> 00:34:56,296

1141
00:34:56,877 --> 00:34:58,147
ที่นี่หรอ

1142
00:34:59,446 --> 00:35:00,394
นะ

1143
00:35:00,408 --> 00:35:00,652

1144
00:35:00,984 --> 00:35:01,279

1145
00:35:01,176 --> 00:35:02,406
วิธีนี้ล่ะ

1146
00:35:02,457 --> 00:35:02,696

1147
00:35:02,585 --> 00:35:02,863

1148
00:35:02,907 --> 00:35:03,218

1149
00:35:03,157 --> 00:35:03,368

1150
00:35:03,477 --> 00:35:03,702

1151
00:35:04,116 --> 00:35:10,277
แบบไหนลูก

1152
00:35:10,845 --> 00:35:14,321
โอเคหาง่ายกว่าเรามาดูตัวอย่าง

1153
00:35:14,426 --> 00:35:14,708

1154
00:35:14,555 --> 00:35:14,821

1155
00:35:15,396 --> 00:35:15,645

1156
00:35:17,504 --> 00:35:19,052
ตัวอย่างก่อนแล้วกันเนาะ

1157
00:35:18,988 --> 00:35:20,337
กลับมาตรงนี้

1158
00:35:20,325 --> 00:35:20,827

1159
00:35:21,097 --> 00:35:21,326

1160
00:35:21,346 --> 00:35:21,582

1161
00:35:21,475 --> 00:35:21,742

1162
00:35:21,668 --> 00:35:26,252
ก็ยังมี 5 ข้อ

1163
00:35:26,226 --> 00:35:26,650

1164
00:35:26,736 --> 00:35:26,973

1165
00:35:26,867 --> 00:35:29,361
จะให้ทำข้อ 5 ก่อน

1166
00:35:29,548 --> 00:35:31,492
ไปทำกับข้าวก่อนนะ

1167
00:35:32,626 --> 00:35:34,616
มองมองมอง

1168
00:35:34,677 --> 00:35:35,959
สะกิดเพื่อนมองหน่อย

1169
00:35:36,216 --> 00:35:36,450

1170
00:35:36,405 --> 00:35:38,622

1171
00:35:38,905 --> 00:35:39,143

1172
00:35:39,284 --> 00:35:42,254
ให้หาคำตอบข้อ 5 ได้

1173
00:35:42,105 --> 00:35:47,414
เขาบอกว่าจงหาผลบวกของ 9 พจน์แรกของ 147

1174
00:35:47,358 --> 00:35:47,873

1175
00:35:49,476 --> 00:35:52,049
ใช้วิธีที่ 2 เมื่อกี้คือหาค่า

1176
00:35:52,034 --> 00:35:52,933
อะไรคะ

1177
00:35:53,124 --> 00:35:53,418

1178
00:35:54,595 --> 00:35:55,746
คดี

1179
00:35:55,815 --> 00:35:56,653
มีทำไง

1180
00:35:56,659 --> 00:35:57,398

1181
00:35:57,356 --> 00:35:58,623
ค้นหาคดี

1182
00:35:58,575 --> 00:35:59,387

1183
00:35:59,537 --> 00:35:59,888

1184
00:35:59,857 --> 00:36:00,134

1185
00:36:00,044 --> 00:36:00,529

1186
00:36:00,565 --> 00:36:03,999
พอดีๆราคาดี

1187
00:36:04,076 --> 00:36:04,366

1188
00:36:07,224 --> 00:36:08,242
ลองไหม

1189
00:36:08,624 --> 00:36:10,791

1190
00:36:10,744 --> 00:36:14,526
ก็จะไปหรอหาคดีออกมาก่อน

1191
00:36:14,466 --> 00:36:19,254
ราคาดีก่อนถ้าดีก่อนถ้าดีข้อนี้คืออะไร

1192
00:36:20,028 --> 00:36:20,315

1193
00:36:20,666 --> 00:36:20,920

1194
00:36:21,704 --> 00:36:22,029

1195
00:36:22,665 --> 00:36:24,886
ดีๆ

1196
00:36:25,227 --> 00:36:25,431

1197
00:36:25,347 --> 00:36:30,591
R35 ดีคือ 3

1198
00:36:30,866 --> 00:36:32,363
สวัสดีค่ะ 3 งั้น

1199
00:36:32,716 --> 00:36:32,988

1200
00:36:33,935 --> 00:36:35,556
ให้เพื่อนดูได้ไหมคะ

1201
00:36:35,985 --> 00:36:37,436
ได้ไหม

1202
00:36:38,357 --> 00:36:38,609

1203
00:36:39,124 --> 00:36:39,881

1204
00:36:39,897 --> 00:36:41,699
ไม่เอาไปให้เพื่อนดูได้ไหม

1205
00:36:42,265 --> 00:36:45,975
งั้นเดี๋ยวขอเวลาสักพักนึงนะคะเดี๋ยวให้เด็กๆทำแบบฝึกหัดนี้ดู

1206
00:36:45,858 --> 00:36:46,087

1207
00:36:46,943 --> 00:36:47,635

1208
00:36:47,644 --> 00:36:48,075

1209
00:36:49,889 --> 00:36:50,148

1210
00:36:50,145 --> 00:36:52,179

1211
00:36:52,124 --> 00:36:52,367

1212
00:36:53,536 --> 00:36:53,786

1213
00:36:58,029 --> 00:36:58,258

1214
00:37:03,916 --> 00:37:04,177

1215
00:37:04,816 --> 00:37:05,094

1216
00:37:05,384 --> 00:37:05,650

1217
00:37:06,285 --> 00:37:06,495

1218
00:37:10,835 --> 00:37:11,073

1219
00:37:27,425 --> 00:37:27,653

1220
00:37:31,524 --> 00:37:31,808

1221
00:37:51,136 --> 00:37:51,525

1222
00:37:56,635 --> 00:37:57,056

1223
00:38:13,543 --> 00:38:13,764

1224
00:38:19,257 --> 00:38:19,512

1225
00:38:38,147 --> 00:38:38,366

1226
00:38:44,946 --> 00:38:45,217

1227
00:39:16,465 --> 00:39:16,698

1228
00:39:28,943 --> 00:39:29,167

1229
00:39:29,334 --> 00:39:29,612

1230
00:39:40,934 --> 00:39:41,211

1231
00:39:47,663 --> 00:39:47,893

1232
00:40:00,212 --> 00:40:00,611

1233
00:40:01,684 --> 00:40:01,942

1234
00:40:11,943 --> 00:40:12,211

1235
00:40:25,134 --> 00:40:25,381

1236
00:40:43,193 --> 00:40:43,617

1237
00:40:46,273 --> 00:40:46,479

1238
00:40:59,985 --> 00:41:00,231

1239
00:41:03,823 --> 00:41:04,106

1240
00:41:05,623 --> 00:41:06,080

1241
00:41:24,782 --> 00:41:25,067

1242
00:41:40,462 --> 00:41:40,743

1243
00:41:50,540 --> 00:41:50,999

1244
00:42:06,422 --> 00:42:06,709

1245
00:42:09,945 --> 00:42:10,343

1246
00:42:44,142 --> 00:42:44,394

1247
00:42:45,942 --> 00:42:46,340

1248
00:43:01,381 --> 00:43:01,605

1249
00:43:01,823 --> 00:43:02,208

1250
00:43:14,004 --> 00:43:14,262

1251
00:43:15,412 --> 00:43:15,698

1252
00:43:15,660 --> 00:43:15,906

1253
00:43:16,691 --> 00:43:16,975

1254
00:43:38,021 --> 00:43:38,225

1255
00:43:38,220 --> 00:43:38,520

1256
00:43:43,870 --> 00:43:44,256

1257
00:44:23,951 --> 00:44:24,243

1258
00:44:37,660 --> 00:44:37,945

1259
00:44:38,430 --> 00:44:38,652

1260
00:44:40,481 --> 00:44:40,932

1261
00:44:44,009 --> 00:44:44,439

1262
00:44:45,930 --> 00:44:46,187

1263
00:44:53,491 --> 00:44:53,884

1264
00:44:59,133 --> 00:44:59,377

1265
00:45:10,223 --> 00:45:10,491

1266
00:45:13,281 --> 00:45:13,499

1267
00:45:17,511 --> 00:45:17,750

1268
00:45:21,743 --> 00:45:21,998

1269
00:46:07,100 --> 00:46:07,383

1270
00:46:28,559 --> 00:46:28,786

1271
00:46:29,458 --> 00:46:29,722

1272
00:46:30,538 --> 00:46:30,834

1273
00:46:30,802 --> 00:46:31,230

1274
00:46:31,252 --> 00:46:31,550

1275
00:46:49,499 --> 00:46:49,787

1276
00:47:03,218 --> 00:47:03,452

1277
00:47:12,179 --> 00:47:12,599

1278
00:47:16,152 --> 00:47:16,584

1279
00:47:30,382 --> 00:47:30,660

1280
00:47:57,022 --> 00:47:57,463

1281
00:48:02,408 --> 00:48:02,688

1282
00:48:07,539 --> 00:48:07,971

1283
00:48:15,859 --> 00:48:16,089

1284
00:48:17,400 --> 00:48:17,636

1285
00:48:38,218 --> 00:48:38,458

1286
00:48:55,326 --> 00:48:55,762

1287
00:49:21,267 --> 00:49:21,508

1288
00:49:31,968 --> 00:49:32,200

1289
00:50:07,579 --> 00:50:07,819

1290
00:50:08,865 --> 00:50:09,115

1291
00:50:09,377 --> 00:50:09,640

1292
00:50:09,510 --> 00:50:09,896

1293
00:50:21,228 --> 00:50:21,643

1294
00:50:48,256 --> 00:50:48,477

1295
00:50:48,966 --> 00:50:49,197

1296
00:50:55,567 --> 00:50:55,802

1297
00:51:13,248 --> 00:51:13,482

1298
00:51:18,056 --> 00:51:18,344

1299
00:51:31,767 --> 00:51:32,016

1300
00:51:35,666 --> 00:51:35,918

1301
00:51:40,216 --> 00:51:40,665

1302
00:52:10,705 --> 00:52:10,993

1303
00:52:28,136 --> 00:52:28,563

1304
00:52:28,455 --> 00:52:28,735

1305
00:52:47,038 --> 00:52:47,286

1306
00:52:47,676 --> 00:52:47,945

1307
00:52:48,578 --> 00:52:48,878

1308
00:53:04,774 --> 00:53:05,062

1309
00:53:39,114 --> 00:53:39,518

1310
00:53:41,417 --> 00:53:41,869

1311
00:53:56,025 --> 00:53:56,310

1312
00:53:56,854 --> 00:53:57,122

1313
00:54:02,304 --> 00:54:02,531

1314
00:54:06,786 --> 00:54:07,025

1315
00:54:07,245 --> 00:54:07,457

1316
00:54:11,215 --> 00:54:11,462

1317
00:54:23,644 --> 00:54:23,894

1318
00:54:44,904 --> 00:54:45,156

1319
00:54:45,934 --> 00:54:46,396

1320
00:54:47,924 --> 00:54:48,248

1321
00:54:48,884 --> 00:54:49,150

1322
00:54:53,234 --> 00:54:53,616

1323
00:55:05,157 --> 00:55:05,415

1324
00:55:07,075 --> 00:55:07,510

1325
00:55:09,895 --> 00:55:10,147

1326
00:55:20,786 --> 00:55:21,203

1327
00:55:20,973 --> 00:55:21,191

1328
00:55:34,933 --> 00:55:35,390

1329
00:55:37,373 --> 00:55:37,608

1330
00:56:13,768 --> 00:56:14,019

1331
00:56:14,786 --> 00:56:15,252

1332
00:56:15,173 --> 00:56:15,433

1333
00:56:15,816 --> 00:56:16,075

1334
00:56:31,313 --> 00:56:31,599

1335
00:56:37,083 --> 00:56:37,353

1336
00:56:46,493 --> 00:56:46,781

1337
00:57:07,252 --> 00:57:07,495

1338
00:57:11,483 --> 00:57:11,943

1339
00:57:12,446 --> 00:57:12,664

1340
00:57:33,845 --> 00:57:34,131

1341
00:58:06,701 --> 00:58:06,933

1342
00:58:08,623 --> 00:58:08,862

1343
00:58:18,492 --> 00:58:18,740

1344
00:58:29,512 --> 00:58:29,941

1345
00:58:35,915 --> 00:58:36,160

1346
00:58:36,042 --> 00:58:36,336

1347
00:58:46,101 --> 00:58:46,550

1348
00:58:46,493 --> 00:58:46,958

1349
00:58:53,922 --> 00:58:54,157

1350
00:59:10,061 --> 00:59:10,285

1351
00:59:21,534 --> 00:59:21,823

1352
00:59:21,911 --> 00:59:22,173

1353
00:59:38,894 --> 00:59:39,161

1354
00:59:43,250 --> 00:59:43,520

1355
00:59:48,050 --> 00:59:48,472

1356
00:59:48,300 --> 00:59:48,557

1357
00:59:48,492 --> 00:59:48,726

1358
00:59:48,692 --> 00:59:48,920

1359
00:59:49,010 --> 00:59:49,297

1360
00:59:49,201 --> 00:59:49,448

1361
00:59:52,980 --> 00:59:53,210

1362
01:00:04,004 --> 01:00:04,298

1363
01:00:19,054 --> 01:00:21,494

1364
01:00:21,613 --> 01:00:22,091

1365
01:00:25,781 --> 01:00:26,033

1366
01:00:31,801 --> 01:00:32,033

1367
01:00:33,280 --> 01:00:33,547

1368
01:00:36,543 --> 01:00:36,987

1369
01:00:52,372 --> 01:00:52,806

1370
01:00:55,953 --> 01:00:56,250

1371
01:00:57,560 --> 01:00:57,843

1372
01:01:00,633 --> 01:01:01,081

1373
01:01:36,691 --> 01:01:36,982

1374
01:01:42,530 --> 01:01:42,781

1375
01:01:47,139 --> 01:01:47,383

1376
01:01:48,870 --> 01:01:49,246

1377
01:02:00,913 --> 01:02:01,166

1378
01:02:01,361 --> 01:02:01,630

1379
01:02:13,600 --> 01:02:13,833

1380
01:02:33,970 --> 01:02:34,219

1381
01:02:43,838 --> 01:02:44,263

1382
01:02:46,269 --> 01:02:46,697

1383
01:02:53,192 --> 01:02:53,583

1384
01:02:58,760 --> 01:02:59,157

1385
01:03:12,208 --> 01:03:12,488

1386
01:03:12,920 --> 01:03:13,207

1387
01:03:13,109 --> 01:03:13,497

1388
01:03:13,373 --> 01:03:13,666

1389
01:03:13,749 --> 01:03:13,994

1390
01:03:14,008 --> 01:03:14,412

1391
01:03:14,128 --> 01:03:14,414

1392
01:03:14,328 --> 01:03:14,564

1393
01:03:19,708 --> 01:03:19,957

1394
01:03:39,369 --> 01:03:39,830

1395
01:03:56,223 --> 01:03:56,686

1396
01:04:02,890 --> 01:04:03,165

1397
01:04:06,028 --> 01:04:06,320

1398
01:04:09,608 --> 01:04:09,989

1399
01:04:10,828 --> 01:04:11,220

1400
01:04:12,238 --> 01:04:12,523

1401
01:04:17,169 --> 01:04:17,442

1402
01:04:18,388 --> 01:04:18,793

1403
01:04:20,688 --> 01:04:20,967

1404
01:04:45,489 --> 01:04:45,734

1405
01:04:55,608 --> 01:04:55,889

1406
01:04:55,738 --> 01:04:55,997

1407
01:04:56,057 --> 01:04:56,344

1408
01:04:56,188 --> 01:04:56,440

1409
01:04:56,568 --> 01:04:57,067

1410
01:04:57,407 --> 01:04:57,695

1411
01:04:57,728 --> 01:04:58,035

1412
01:04:58,050 --> 01:04:58,286

1413
01:05:04,967 --> 01:05:05,240

1414
01:05:15,597 --> 01:05:15,875

1415
01:05:17,578 --> 01:05:18,035

1416
01:05:19,767 --> 01:05:20,000

1417
01:05:20,146 --> 01:05:20,554

1418
01:05:20,598 --> 01:05:20,999

1419
01:05:26,168 --> 01:05:26,583

1420
01:05:26,867 --> 01:05:27,109

1421
01:05:32,060 --> 01:05:32,345

1422
01:05:33,089 --> 01:05:33,512

1423
01:05:33,847 --> 01:05:34,078

1424
01:05:44,937 --> 01:05:45,195

1425
01:05:50,450 --> 01:05:50,716

1426
01:05:56,407 --> 01:05:56,700

1427
01:05:57,936 --> 01:05:58,169

1428
01:05:58,579 --> 01:05:58,859

1429
01:06:04,537 --> 01:06:04,982

1430
01:06:09,667 --> 01:06:09,906

1431
01:06:10,367 --> 01:06:10,591

1432
01:06:10,888 --> 01:06:11,096

1433
01:06:15,747 --> 01:06:15,976

1434
01:06:30,548 --> 01:06:30,838

1435
01:06:35,999 --> 01:06:36,230

1436
01:06:58,039 --> 01:06:58,486

1437
01:07:05,647 --> 01:07:05,950

1438
01:07:15,400 --> 01:07:15,625

1439
01:07:15,590 --> 01:07:15,807

1440
01:07:28,586 --> 01:07:29,048

1441
01:07:31,726 --> 01:07:32,120

1442
01:07:34,355 --> 01:07:34,632

1443
01:07:35,130 --> 01:07:35,358

1444
01:07:35,380 --> 01:07:35,585

1445
01:07:36,465 --> 01:07:36,674

1446
01:07:44,985 --> 01:07:45,231

1447
01:07:48,835 --> 01:07:49,267

1448
01:07:50,686 --> 01:07:50,924

1449
01:07:51,076 --> 01:07:51,313

1450
01:07:54,976 --> 01:07:55,198

1451
01:07:56,267 --> 01:07:56,551

1452
01:08:20,926 --> 01:08:21,204

1453
01:08:24,579 --> 01:08:24,808

1454
01:08:25,665 --> 01:08:25,891

1455
01:08:43,538 --> 01:08:43,834

1456
01:08:44,765 --> 01:08:45,037

1457
01:08:45,145 --> 01:08:45,390

1458
01:09:01,546 --> 01:09:01,848

1459
01:09:19,610 --> 01:09:20,059

1460
01:09:26,014 --> 01:09:26,439

1461
01:09:36,906 --> 01:09:37,126

1462
01:09:43,376 --> 01:09:43,636

1463
01:09:44,206 --> 01:09:44,454

1464
01:10:08,165 --> 01:10:08,417

1465
01:10:10,026 --> 01:10:10,255

1466
01:10:21,044 --> 01:10:22,056

1467
01:10:22,325 --> 01:10:22,579

1468
01:10:22,574 --> 01:10:22,876

1469
01:10:22,773 --> 01:10:23,217

1470
01:10:23,165 --> 01:10:23,553

1471
01:10:24,313 --> 01:10:25,773

1472
01:10:26,294 --> 01:10:28,714

1473
01:10:31,486 --> 01:10:33,841

1474
01:10:36,674 --> 01:10:38,899

1475
01:10:41,925 --> 01:10:42,350

1476
01:10:53,776 --> 01:10:54,029

1477
01:11:02,233 --> 01:11:02,513

1478
01:11:03,644 --> 01:11:03,873

1479
01:11:04,034 --> 01:11:04,273

1480
01:11:04,284 --> 01:11:04,715

1481
01:11:13,707 --> 01:11:13,953

1482
01:11:16,136 --> 01:11:16,560

1483
01:11:16,905 --> 01:11:17,346

1484
01:11:17,224 --> 01:11:17,439

1485
01:11:27,723 --> 01:11:27,943

1486
01:11:28,885 --> 01:11:29,097

1487
01:11:30,485 --> 01:11:30,889

1488
01:11:30,615 --> 01:11:30,864

1489
01:11:31,254 --> 01:11:31,658

1490
01:11:40,226 --> 01:11:40,705

1491
01:11:40,674 --> 01:11:40,887

1492
01:11:42,725 --> 01:11:43,189

1493
01:11:51,114 --> 01:11:51,359

1494
01:11:55,024 --> 01:11:55,281

1495
01:11:56,174 --> 01:11:56,617

1496
01:11:57,642 --> 01:11:57,920

1497
01:11:58,738 --> 01:11:59,021

1498
01:11:59,244 --> 01:11:59,661

1499
01:11:59,563 --> 01:11:59,854

1500
01:12:00,593 --> 01:12:00,876

1501
01:12:08,342 --> 01:12:08,784

1502
01:12:34,682 --> 01:12:34,977

1503
01:12:34,933 --> 01:12:35,179

1504
01:12:35,643 --> 01:12:35,857

1505
01:12:38,393 --> 01:12:38,619

1506
01:12:41,274 --> 01:12:41,516

1507
01:12:47,487 --> 01:12:47,761

1508
01:12:47,743 --> 01:12:47,963

1509
01:12:47,874 --> 01:12:48,268

1510
01:12:54,535 --> 01:12:54,790

1511
01:12:55,435 --> 01:12:55,720

1512
01:12:56,968 --> 01:12:57,195

1513
01:12:57,484 --> 01:12:57,776

1514
01:12:58,834 --> 01:12:59,148

1515
01:13:16,832 --> 01:13:17,119

1516
01:13:18,563 --> 01:13:18,780

1517
01:13:18,882 --> 01:13:19,150

1518
01:13:19,002 --> 01:13:19,253

1519
01:13:19,262 --> 01:13:19,496

1520
01:13:19,522 --> 01:13:19,765

1521
01:13:20,994 --> 01:13:21,205

1522
01:13:22,654 --> 01:13:22,900

1523
01:13:28,292 --> 01:13:28,748

1524
01:13:30,281 --> 01:13:30,548

1525
01:13:31,632 --> 01:13:31,863

1526
01:13:37,522 --> 01:13:37,778

1527
01:13:42,004 --> 01:13:42,289

1528
01:13:43,353 --> 01:13:43,603

1529
01:13:44,691 --> 01:13:44,939

1530
01:13:50,017 --> 01:13:50,238

1531
01:13:54,814 --> 01:13:55,028

1532
01:13:56,932 --> 01:13:57,193

1533
01:14:01,803 --> 01:14:02,228

1534
01:14:01,994 --> 01:14:02,428

1535
01:14:17,304 --> 01:14:17,573

1536
01:14:25,954 --> 01:14:26,222

1537
01:14:26,204 --> 01:14:26,481

1538
01:14:26,973 --> 01:14:27,252

1539
01:14:28,255 --> 01:14:28,535

1540
01:14:31,653 --> 01:14:32,123

1541
01:14:34,284 --> 01:14:34,505

1542
01:14:34,661 --> 01:14:34,872

1543
01:14:36,714 --> 01:14:37,097

1544
01:14:44,014 --> 01:14:44,288

1545
01:14:52,662 --> 01:14:52,919

1546
01:15:00,992 --> 01:15:01,285

1547
01:15:01,374 --> 01:15:01,597

1548
01:15:02,601 --> 01:15:02,856

1549
01:15:04,906 --> 01:15:05,188

1550
01:15:06,312 --> 01:15:06,628

1551
01:15:06,880 --> 01:15:07,159

1552
01:15:08,682 --> 01:15:08,905

1553
01:15:09,191 --> 01:15:09,476

1554
01:15:17,972 --> 01:15:18,238

1555
01:15:41,352 --> 01:15:41,621

1556
01:15:51,161 --> 01:15:51,426

1557
01:15:58,972 --> 01:15:59,198

1558
01:16:16,840 --> 01:16:17,113

1559
01:16:17,932 --> 01:16:18,162

1560
01:16:22,601 --> 01:16:22,872

1561
01:16:23,181 --> 01:16:23,724

1562
01:16:41,510 --> 01:16:41,766

1563
01:16:45,602 --> 01:16:45,830

1564
01:16:47,208 --> 01:16:47,429

1565
01:16:47,460 --> 01:16:47,736

1566
01:16:55,340 --> 01:16:55,578

1567
01:17:04,440 --> 01:17:04,857

1568
01:17:13,281 --> 01:17:13,565

1569
01:17:21,679 --> 01:17:21,955

1570
01:17:25,773 --> 01:17:25,995

1571
01:17:26,800 --> 01:17:27,054

1572
01:17:28,460 --> 01:17:28,716

1573
01:17:29,300 --> 01:17:29,789

1574
01:17:33,401 --> 01:17:33,622

1575
01:17:39,679 --> 01:17:39,906

1576
01:17:40,639 --> 01:17:40,910

1577
01:17:43,129 --> 01:17:43,354

1578
01:17:47,040 --> 01:17:47,494

1579
01:17:47,558 --> 01:17:47,830

1580
01:17:53,640 --> 01:17:53,847

1581
01:17:58,831 --> 01:17:59,067

1582
01:18:12,479 --> 01:18:12,734

1583
01:18:14,142 --> 01:18:14,409

1584
01:18:14,522 --> 01:18:14,797

1585
01:18:15,422 --> 01:18:15,700

1586
01:18:15,610 --> 01:18:15,871

1587
01:18:25,671 --> 01:18:25,939

1588
01:18:25,922 --> 01:18:26,150

1589
01:18:26,440 --> 01:18:26,695

1590
01:18:41,433 --> 01:18:44,363
load Test

1591
01:18:44,318 --> 01:18:44,570

1592
01:18:44,831 --> 01:18:45,103

1593
01:18:47,200 --> 01:18:47,743

1594
01:18:47,769 --> 01:18:53,124
โอเคนะคะเมื่อกี้ลูกๆก็ได้ทำแบบทดสอบไปทั้ง 3 ข้อ

1595
01:18:53,410 --> 01:18:56,419
ซึ่งครูเจนเดินดูแล้วส่วนใหญ่ก็คือ

1596
01:18:56,480 --> 01:18:57,255
ได้

1597
01:18:57,569 --> 01:18:58,385
เข้าใจ

1598
01:18:58,919 --> 01:19:01,321
มีแค่บางคนเท่านั้นที่จะช้า

1599
01:19:01,609 --> 01:19:03,847
อธิบายก็คือก็เข้าใจ

1600
01:19:03,980 --> 01:19:04,365

1601
01:19:04,429 --> 01:19:05,507
นาทีนี้

1602
01:19:05,709 --> 01:19:07,179
เรามาสรุป

1603
01:19:07,372 --> 01:19:09,938
น้าสรุปการหาผลบวก

1604
01:19:09,998 --> 01:19:10,753
ลำดับ

1605
01:19:11,158 --> 01:19:14,677
ไหมคะหรือการหาค่าของอนุกรม

1606
01:19:14,928 --> 01:19:16,993
ของลำดับที่โจทย์กำหนดมาให้

1607
01:19:17,120 --> 01:19:17,394

1608
01:19:17,309 --> 01:19:19,547
วิธีที่ลูกๆเลือก

1609
01:19:19,680 --> 01:19:20,070

1610
01:19:20,251 --> 01:19:24,102
ทำแล้วรู้สึกว่าทำแล้วเข้าใจง่ายหาคำตอบให้เร็ว

1611
01:19:24,101 --> 01:19:24,362

1612
01:19:24,358 --> 01:19:26,712
คือวิธีนี้ถูกไหมคะคือ

1613
01:19:26,600 --> 01:19:27,552
การหา

1614
01:19:27,561 --> 01:19:29,691
ผลต่างร่วมหรือหาค่าดี

1615
01:19:29,598 --> 01:19:30,045

1616
01:19:30,053 --> 01:19:30,334

1617
01:19:30,498 --> 01:19:31,390
ใช่ไหมคะ

1618
01:19:31,459 --> 01:19:31,709

1619
01:19:31,718 --> 01:19:33,949
อะไรคนเลือกวิธีนี้

1620
01:19:33,961 --> 01:19:35,229

1621
01:19:35,311 --> 01:19:36,588
วันนี้มาดู

1622
01:19:36,589 --> 01:19:40,755
มาเช็คความเข้าใจกันอีกครั้งหนึ่งคุณเจนมีจดบนกระดานให้ 2 ข้อ

1623
01:19:41,517 --> 01:19:41,773

1624
01:19:41,718 --> 01:19:42,650

1625
01:19:42,741 --> 01:19:42,986

1626
01:19:42,998 --> 01:19:43,264

1627
01:19:43,121 --> 01:19:43,527

1628
01:19:43,889 --> 01:19:44,096

1629
01:19:45,428 --> 01:19:47,297
ดูที่โจทก์นะ

1630
01:19:47,667 --> 01:19:51,261
จงหาผลบวกของ 5 พจน์แรกของ 258

1631
01:19:52,028 --> 01:19:52,293

1632
01:19:52,348 --> 01:19:56,853
มีลูกๆเนี่ยเลือกใช้วิธีการหาคำตอบ

1633
01:19:56,839 --> 01:19:57,345

1634
01:19:57,028 --> 01:19:57,277

1635
01:19:57,279 --> 01:19:58,499
น้าโดย

1636
01:19:58,497 --> 01:20:00,423
โดยการหาค่า D

1637
01:20:00,607 --> 01:20:00,838

1638
01:20:01,120 --> 01:20:02,203
ออกมาก่อน

1639
01:20:02,399 --> 01:20:03,930

1640
01:20:03,999 --> 01:20:04,304

1641
01:20:04,639 --> 01:20:07,096
ถ้าดีจำให้ขึ้นใจนะ

1642
01:20:07,020 --> 01:20:10,993
กลับไปที่โรงเรียนเรื่องนี้นะคะเราต้องรู้ว่าค่า Dr ยังไง

1643
01:20:10,859 --> 01:20:11,304

1644
01:20:12,137 --> 01:20:14,409
คุณยายมั่นใจว่าหลายคนถ้าเกิด

1645
01:20:14,319 --> 01:20:15,345
ทำบ่อย

1646
01:20:15,350 --> 01:20:15,636

1647
01:20:15,601 --> 01:20:16,682
ทำไปบ่อย

1648
01:20:16,818 --> 01:20:19,581
จะเก่งจะเข้าใจแล้วก็จะจดจำได้

1649
01:20:19,568 --> 01:20:22,118
โจทย์ข้อนี้ค่ะลูก

1650
01:20:22,399 --> 01:20:22,616

1651
01:20:24,188 --> 01:20:25,791
258

1652
01:20:26,168 --> 01:20:28,919
ลองดูนะ 2558

1653
01:20:29,369 --> 01:20:29,584

1654
01:20:31,301 --> 01:20:33,367
มีค่าดีเท่าไหร่คะ

1655
01:20:33,277 --> 01:20:34,879
ถ้ามองด้วยตา

1656
01:20:34,817 --> 01:20:36,746
258

1657
01:20:36,797 --> 01:20:37,066

1658
01:20:37,246 --> 01:20:37,522

1659
01:20:37,640 --> 01:20:37,891

1660
01:20:37,768 --> 01:20:39,109
25

1661
01:20:39,309 --> 01:20:40,107
แปะ

1662
01:20:41,039 --> 01:20:42,115

1663
01:20:42,059 --> 01:20:42,575

1664
01:20:42,697 --> 01:20:42,936

1665
01:20:42,889 --> 01:20:44,881
ถ้าดีมีค่าเท่าไหร่คะ

1666
01:20:45,258 --> 01:20:46,563
ไอ้นึกได้

1667
01:20:46,998 --> 01:20:47,431

1668
01:20:47,321 --> 01:20:49,238
ถูกต้อง

1669
01:20:49,243 --> 01:20:50,110
ใช่ไหม

1670
01:20:50,448 --> 01:20:51,475
ที่ดีๆ

1671
01:20:52,238 --> 01:20:56,637
258 ฮ่าๆๆ

1672
01:20:56,670 --> 01:20:57,484

1673
01:20:57,557 --> 01:20:57,771

1674
01:20:57,956 --> 01:20:58,385

1675
01:20:58,778 --> 01:21:01,186
แปะ

1676
01:21:01,208 --> 01:21:02,281

1677
01:21:02,367 --> 01:21:04,109
คดีคดี

1678
01:21:04,607 --> 01:21:08,169
อย่าลืมราคาดีคือเรานำตัวเลขที่อยู่ใกล้กันนะลูก

1679
01:21:08,517 --> 01:21:10,111
อยู่ใกล้กัน

1680
01:21:10,308 --> 01:21:11,917
ตัวหน้า

1681
01:21:12,238 --> 01:21:12,987

1682
01:21:13,129 --> 01:21:13,428

1683
01:21:13,449 --> 01:21:14,790
5 กับ 8

1684
01:21:16,518 --> 01:21:17,643
คู่ไหนล่ะ

1685
01:21:17,610 --> 01:21:18,928
กู 5 นี้ใช่ไหม

1686
01:21:19,730 --> 01:21:20,749

1687
01:21:20,687 --> 01:21:24,013
คดีมีค่าเท่ากับ 3 ถูกต้องค่ะ

1688
01:21:24,210 --> 01:21:29,851
พอเราได้ค่าดีแล้วนะคะมีค่าเท่ากับ 3 เราก็มาหา

1689
01:21:30,747 --> 01:21:33,308
ถ้าพจน์ที่โจทย์กำหนดถูกไหมคะ

1690
01:21:33,688 --> 01:21:35,581
ทั้ง 5 พจน์ที่โจทย์กำหนด

1691
01:21:35,621 --> 01:21:36,966
แล้วก็หาคำตอบ

1692
01:21:36,957 --> 01:21:38,293
ของอนุกรมออกมา

1693
01:21:38,947 --> 01:21:39,158

1694
01:21:39,588 --> 01:21:39,828

1695
01:21:40,098 --> 01:21:43,238
ดีไหมคะดูโจทย์ข้อนี้บนกระดานค่ะ

1696
01:21:44,456 --> 01:21:47,803
โจทย์คณิตบนกระดานใครหาคำตอบให้คุณจะได้บ้าง

1697
01:21:47,655 --> 01:21:47,880

1698
01:21:47,918 --> 01:21:48,136

1699
01:21:48,168 --> 01:21:48,396

1700
01:21:48,877 --> 01:21:49,751

1701
01:21:49,957 --> 01:21:51,622
มีคะแนนให้นะคะ

1702
01:21:51,699 --> 01:21:53,113
มีคะแนนให้เลยนะ

1703
01:21:53,299 --> 01:21:55,414
ข้อละ 10 คะแนนไปเลย

1704
01:21:55,856 --> 01:21:56,093

1705
01:21:56,498 --> 01:21:58,048
ข้อละ 10 คะแนน

1706
01:21:57,967 --> 01:21:58,349

1707
01:21:58,357 --> 01:21:58,980

1708
01:21:58,930 --> 01:21:59,150

1709
01:21:59,768 --> 01:22:01,435

1710
01:22:01,438 --> 01:22:01,751

1711
01:22:01,758 --> 01:22:02,765

1712
01:22:03,287 --> 01:22:03,579

1713
01:22:03,546 --> 01:22:05,014
เข้าใจไหมคะ

1714
01:22:05,337 --> 01:22:05,974

1715
01:22:06,113 --> 01:22:06,589

1716
01:22:06,559 --> 01:22:08,477
ใจออกมาไม่จอย

1717
01:22:08,866 --> 01:22:09,622

1718
01:22:09,696 --> 01:22:10,210

1719
01:22:10,208 --> 01:22:12,707

1720
01:22:12,959 --> 01:22:15,839
มาทำให้ดูหน่อย

1721
01:22:16,107 --> 01:22:16,325

1722
01:22:16,558 --> 01:22:16,840

1723
01:22:17,707 --> 01:22:18,011

1724
01:22:18,408 --> 01:22:18,690

1725
01:22:18,539 --> 01:22:18,797

1726
01:22:19,117 --> 01:22:19,373

1727
01:22:19,561 --> 01:22:20,381

1728
01:22:20,516 --> 01:22:20,767

1729
01:22:20,721 --> 01:22:21,338

1730
01:22:21,546 --> 01:22:22,684

1731
01:22:22,696 --> 01:22:25,451

1732
01:22:25,586 --> 01:22:25,906

1733
01:22:25,907 --> 01:22:28,352
แล้วมาดูกันนะคะว่า

1734
01:22:28,275 --> 01:22:28,521

1735
01:22:28,657 --> 01:22:28,955

1736
01:22:29,036 --> 01:22:33,864
เพื่อนออกมาทำโจทย์บนกระดานลูกๆก็ทำในสมุด

1737
01:22:33,977 --> 01:22:34,545

1738
01:22:34,806 --> 01:22:37,231
ทำในสมุดด้วย

1739
01:22:37,175 --> 01:22:37,645

1740
01:22:37,501 --> 01:22:37,788

1741
01:22:37,949 --> 01:22:39,854

1742
01:22:40,000 --> 01:22:40,499

1743
01:22:40,768 --> 01:22:41,016

1744
01:22:41,536 --> 01:22:41,827

1745
01:22:41,856 --> 01:22:42,141

1746
01:22:42,305 --> 01:22:42,766

1747
01:22:42,755 --> 01:22:45,752
เรามาดูคำตอบเรากับเพื่อนจะตรงกันไหม

1748
01:22:45,697 --> 01:22:46,123

1749
01:22:46,528 --> 01:22:48,442
ไม่

1750
01:22:48,447 --> 01:22:50,788
ตกลงสินค้าตัวเดียวกัน

1751
01:22:50,828 --> 01:22:51,041

1752
01:22:50,957 --> 01:22:52,604
ตัวเดียวกันตั้งกล้อง

1753
01:22:52,616 --> 01:22:52,828

1754
01:22:53,069 --> 01:22:54,659

1755
01:22:54,859 --> 01:22:57,101
อย่าลืมนะคะการหาค่า D

1756
01:22:57,109 --> 01:22:58,388
ปัญหาคดี

1757
01:22:58,446 --> 01:22:58,706

1758
01:22:59,477 --> 01:23:01,449
แค่จับคู่

1759
01:23:01,459 --> 01:23:04,215
ลำดับที่อยู่ใกล้กันมา

1760
01:23:04,276 --> 01:23:04,500

1761
01:23:04,716 --> 01:23:08,865
นะจับคู่ลำดับที่อยู่ใกล้กันมา 1 คู่ใช่ไหมคะ

1762
01:23:08,756 --> 01:23:09,637
นำ

1763
01:23:10,675 --> 01:23:13,180
ตัวเลขที่อยู่ข้างหลังตัวเลขที่ทํานาย

1764
01:23:13,368 --> 01:23:14,910
มันคือการหาค่า D

1765
01:23:15,106 --> 01:23:16,798
หนา

1766
01:23:17,668 --> 01:23:18,119

1767
01:23:18,556 --> 01:23:18,940

1768
01:23:20,037 --> 01:23:20,484

1769
01:23:20,418 --> 01:23:20,657

1770
01:23:21,118 --> 01:23:23,297
จากนั้นเราก็หาผลบวก

1771
01:23:23,499 --> 01:23:25,864
ของโพสต์ตามที่โจทย์กำหนดให้เลย

1772
01:23:26,636 --> 01:23:27,102

1773
01:23:28,106 --> 01:23:28,925

1774
01:23:30,420 --> 01:23:31,941

1775
01:23:31,956 --> 01:23:32,628

1776
01:23:32,596 --> 01:23:37,494
น้าจากลำดับ 2558 นะคะเพื่อนหาค่าได้คือสาร

1777
01:23:37,328 --> 01:23:39,803
งั้นจาก 258

1778
01:23:39,836 --> 01:23:40,971
ต่อไปก็คือ

1779
01:23:40,916 --> 01:23:41,684
11

1780
01:23:42,008 --> 01:23:42,262

1781
01:23:42,396 --> 01:23:43,443
สี

1782
01:23:43,926 --> 01:23:45,275
สภาพรถหรือยัง

1783
01:23:45,845 --> 01:23:51,604
ถ้าพจน์แล้วจากนั้นเราก็หาค่าของอนุกรมได้เลยค่ะโดยนำแต่ละคนมาทำอะไรกันคะ

1784
01:23:51,997 --> 01:23:53,211
บวกกัน

1785
01:23:53,667 --> 01:23:55,529
นำแต่ละพจน์มาบวกกัน

1786
01:23:55,526 --> 01:23:55,749

1787
01:23:55,656 --> 01:23:55,939

1788
01:23:55,846 --> 01:23:56,929

1789
01:23:57,065 --> 01:23:57,306

1790
01:23:57,256 --> 01:24:00,654
2 + 5 + 8 + 11

1791
01:24:00,716 --> 01:24:02,312
และ + 14

1792
01:24:02,505 --> 01:24:02,771

1793
01:24:02,636 --> 01:24:02,867

1794
01:24:03,087 --> 01:24:03,312

1795
01:24:03,538 --> 01:24:04,060

1796
01:24:04,116 --> 01:24:04,483

1797
01:24:04,687 --> 01:24:07,526
2 + 5 เท่าไหร่คะ 2

1798
01:24:07,756 --> 01:24:08,644
+

1799
01:24:08,595 --> 01:24:09,792

1800
01:24:09,935 --> 01:24:10,392

1801
01:24:10,445 --> 01:24:13,152
เจ็บไหมคะ

1802
01:24:13,205 --> 01:24:14,426
Spy

1803
01:24:14,485 --> 01:24:14,771

1804
01:24:15,259 --> 01:24:16,080
7

1805
01:24:16,154 --> 01:24:17,358
+

1806
01:24:17,305 --> 01:24:19,018
8

1807
01:24:19,878 --> 01:24:22,702
ถูกต้องค่ะ 10-15 ใช้ค่ะ

1808
01:24:22,686 --> 01:24:22,992

1809
01:24:24,286 --> 01:24:25,448
ป้าย

1810
01:24:25,566 --> 01:24:27,684
15 + 11 -

1811
01:24:27,627 --> 01:24:28,010

1812
01:24:28,456 --> 01:24:30,492
15 +

1813
01:24:30,758 --> 01:24:32,150
11

1814
01:24:32,167 --> 01:24:32,386

1815
01:24:32,357 --> 01:24:32,658

1816
01:24:34,027 --> 01:24:34,998

1817
01:24:35,757 --> 01:24:37,555
15 +

1818
01:24:38,195 --> 01:24:40,030
11

1819
01:24:41,266 --> 01:24:41,640

1820
01:24:41,586 --> 01:24:42,796
อะไรนะ

1821
01:24:43,638 --> 01:24:43,883

1822
01:24:43,840 --> 01:24:44,076

1823
01:24:44,214 --> 01:24:44,857

1824
01:24:45,755 --> 01:24:47,214
20 เท่าไหร่

1825
01:24:47,674 --> 01:24:48,029

1826
01:24:48,506 --> 01:24:48,742

1827
01:24:48,695 --> 01:24:48,933

1828
01:24:48,824 --> 01:24:49,097

1829
01:24:49,395 --> 01:24:51,107
25 ใหญ่

1830
01:24:51,067 --> 01:24:51,575

1831
01:24:52,035 --> 01:24:52,466

1832
01:24:52,416 --> 01:24:53,811
15

1833
01:24:53,824 --> 01:24:54,849
+

1834
01:24:54,785 --> 01:25:00,067
11 จะไปแข่งบวกบวกเลขเร็วนะเนี่ย

1835
01:25:00,105 --> 01:25:01,508
5 + 11

1836
01:25:01,705 --> 01:25:02,720
เมื่อไหร่

1837
01:25:02,985 --> 01:25:03,242

1838
01:25:03,626 --> 01:25:04,007

1839
01:25:04,397 --> 01:25:04,617

1840
01:25:04,965 --> 01:25:05,525

1841
01:25:05,606 --> 01:25:05,847

1842
01:25:05,864 --> 01:25:09,956
15 + 11

1843
01:25:10,227 --> 01:25:11,552
20 เท่าไหร่

1844
01:25:11,755 --> 01:25:12,019

1845
01:25:11,884 --> 01:25:15,352
26 26 + 14

1846
01:25:16,045 --> 01:25:16,312

1847
01:25:16,755 --> 01:25:18,924
26

1848
01:25:19,127 --> 01:25:19,423

1849
01:25:19,445 --> 01:25:20,249
+

1850
01:25:20,535 --> 01:25:21,269
10

1851
01:25:21,176 --> 01:25:22,130
4

1852
01:25:22,264 --> 01:25:22,580

1853
01:25:22,714 --> 01:25:23,067

1854
01:25:23,415 --> 01:25:23,848

1855
01:25:23,995 --> 01:25:24,754

1856
01:25:24,833 --> 01:25:25,393

1857
01:25:25,344 --> 01:25:26,306

1858
01:25:26,235 --> 01:25:27,128

1859
01:25:27,074 --> 01:25:27,584

1860
01:25:27,513 --> 01:25:27,910

1861
01:25:27,964 --> 01:25:30,633
26 + 14

1862
01:25:30,786 --> 01:25:31,078

1863
01:25:31,106 --> 01:25:33,114
คิดๆๆ

1864
01:25:35,596 --> 01:25:37,751
นี่

1865
01:25:37,765 --> 01:25:38,199

1866
01:25:38,274 --> 01:25:39,889

1867
01:25:39,877 --> 01:25:40,513

1868
01:25:41,294 --> 01:25:41,572

1869
01:25:41,619 --> 01:25:41,881

1870
01:25:41,874 --> 01:25:42,500

1871
01:25:42,518 --> 01:25:47,812
40 ถูกไหมคะถูกต้องเพื่อนหน่อยค่ะ

1872
01:25:47,825 --> 01:25:53,207
โอเคนะคะจากตรงนี้นะคะ

1873
01:25:55,765 --> 01:25:56,479

1874
01:25:56,534 --> 01:25:58,818
คุณเจนเห็นแล้วว่า

1875
01:25:59,035 --> 01:25:59,314

1876
01:25:59,296 --> 01:26:00,829
ส่วนใหญ่เข้าใจ

1877
01:26:01,478 --> 01:26:07,014
เข้าใจวิธีหาเนาะวิธีหาอนุกรมโดยการหาค่าดีจึงนี้นะคะ

1878
01:26:06,854 --> 01:26:09,470
อาจจะต้องไปฝึกฝนในเรื่องการบวกเลข

1879
01:26:09,355 --> 01:26:09,580

1880
01:26:09,603 --> 01:26:09,820

1881
01:26:09,794 --> 01:26:10,033

1882
01:26:10,565 --> 01:26:11,524
อยู่ไหน

1883
01:26:11,464 --> 01:26:12,485
ดูนะ

1884
01:26:13,384 --> 01:26:17,186
ทุกคนนะฮะเกือบทุกคนเลยต้องไปฝึกฝนเรื่องการบวกเลข

1885
01:26:17,105 --> 01:26:17,536

1886
01:26:17,744 --> 01:26:19,626
เรื่องการบวกเลข

1887
01:26:19,536 --> 01:26:19,764

1888
01:26:19,663 --> 01:26:19,938

1889
01:26:20,365 --> 01:26:22,411
ไม่ต้องบวกให้

1890
01:26:22,995 --> 01:26:25,778
ต้องบวกให้คล่องนะคะต้องบวกให้คล่องเนาะ

1891
01:26:26,073 --> 01:26:26,291

1892
01:26:26,267 --> 01:26:28,927
โอเคนะคะสำหรับวันนี้นะคะ

1893
01:26:29,014 --> 01:26:31,528
ตามจุดประสงค์ของเราคือ 1 ลูกๆ

1894
01:26:31,644 --> 01:26:35,618
รู้ว่าลูกอมคืออะไรอนุกรมก็คือผลบวกของลำดับ

1895
01:26:35,874 --> 01:26:36,114

1896
01:26:36,067 --> 01:26:37,021
ได้ไหมคะ

1897
01:26:36,953 --> 01:26:37,229

1898
01:26:37,665 --> 01:26:40,699
ลูกๆสามารถหาผลบวกของ

1899
01:26:40,674 --> 01:26:42,074
คนที่อ่านได้

1900
01:26:42,346 --> 01:26:45,849
ถือว่าโอเคบรรลุเป้าหมายเพราะวันนี้นะคะ

1901
01:26:45,864 --> 01:26:46,142

1902
01:26:46,247 --> 01:26:48,702
วันนี้ก็หมดเวลาแล้วใช่ไหมคะ

1903
01:26:49,003 --> 01:26:50,983
หมดเวลาแล้วเดี๋ยวลูกๆ

1904
01:26:51,183 --> 01:26:53,489
แล้วขอบคุณที่ล่ามค่ะลูก

1905
01:26:53,483 --> 01:26:53,753

1906
01:26:54,254 --> 01:26:54,636

1907
01:26:54,763 --> 01:26:56,223

1908
01:26:56,183 --> 01:26:56,461

1909
01:26:56,375 --> 01:26:56,765

1910
01:26:56,694 --> 01:26:57,419

1911
01:26:57,394 --> 01:26:57,659

1912
01:26:57,713 --> 01:27:03,004
ลูกค้าใช้ขอบคุณพี่ล่างก่อน

1913
01:27:03,105 --> 01:27:05,661
จ้าขอบคุณมากค่ะ

1914
01:27:05,913 --> 01:27:06,432

1915
01:27:06,623 --> 01:27:07,890

1916
01:27:07,835 --> 01:27:08,590

1917
01:27:10,593 --> 01:27:12,181

1918
01:27:19,043 --> 01:27:19,275

1919
01:27:20,206 --> 01:27:20,439

1920
01:27:21,934 --> 01:27:22,211

1921
01:27:24,753 --> 01:27:24,986

1922
01:27:27,894 --> 01:27:28,178

1923
01:27:32,501 --> 01:27:32,776

1924
01:27:34,674 --> 01:27:34,904

1925
01:27:35,514 --> 01:27:35,776

1926
01:27:37,114 --> 01:27:37,386

1927
01:27:43,582 --> 01:27:43,839

1928
01:27:43,777 --> 01:27:44,027

1929
01:27:44,294 --> 01:27:44,546

1930
01:27:46,404 --> 01:27:46,658

1931
01:27:48,263 --> 01:27:48,519

1932
01:27:51,463 --> 01:27:51,679

1933
01:27:55,073 --> 01:27:55,500

1934
01:27:56,781 --> 01:27:56,999

1935
01:28:01,972 --> 01:28:02,251

1936
01:28:05,304 --> 01:28:05,532

1937
01:28:06,134 --> 01:28:06,382

1938
01:28:06,261 --> 01:28:06,718

1939
01:28:08,634 --> 01:28:08,915

1940
01:28:09,664 --> 01:28:09,941

1941
01:28:11,772 --> 01:28:12,002

1942
01:28:15,673 --> 01:28:15,963

1943
01:28:16,073 --> 01:28:16,312

1944
01:28:25,612 --> 01:28:25,895

1945
01:28:26,252 --> 01:28:26,508

1946
01:28:26,633 --> 01:28:26,921

1947
01:28:27,402 --> 01:28:27,615

1948
01:28:29,777 --> 01:28:30,057

1949
01:28:30,994 --> 01:28:31,250

1950
01:28:31,562 --> 01:28:31,846

1951
01:28:31,752 --> 01:28:31,985

1952
01:28:31,952 --> 01:28:32,217

1953
01:28:41,633 --> 01:28:41,885

1954
01:28:43,611 --> 01:28:43,892

1955
01:28:46,112 --> 01:28:46,385

1956
01:28:46,492 --> 01:28:46,714

1957
01:28:46,622 --> 01:28:46,849

1958
01:28:47,191 --> 01:28:47,408

1959
01:28:48,032 --> 01:28:48,282

1960
01:28:48,603 --> 01:28:48,835

1961
01:28:48,735 --> 01:28:49,009

1962
01:28:59,565 --> 01:28:59,809

1963
01:29:05,193 --> 01:29:05,435

1964
01:29:06,552 --> 01:29:06,798

1965
01:29:11,473 --> 01:29:11,761

1966
01:29:11,861 --> 01:29:12,104

1967
01:29:13,594 --> 01:29:13,817

1968
01:29:15,071 --> 01:29:15,329

1969
01:29:15,513 --> 01:29:15,808

1970
01:29:15,833 --> 01:29:16,087

1971
01:29:16,412 --> 01:29:16,676

1972
01:29:16,731 --> 01:29:16,976

1973
01:29:17,376 --> 01:29:17,597

1974
01:29:17,561 --> 01:29:17,795

1975
01:29:18,011 --> 01:29:18,287

1976
01:29:22,693 --> 01:29:22,971

1977
01:29:26,660 --> 01:29:26,880

1978
01:29:29,608 --> 01:29:29,889

1979
01:29:30,890 --> 01:29:31,140

1980
01:29:35,503 --> 01:29:35,727

1981
01:29:35,691 --> 01:29:35,907

1982
01:29:36,911 --> 01:29:37,167

1983
01:29:37,671 --> 01:29:37,873

1984
01:29:38,254 --> 01:29:38,506

1985
01:29:39,362 --> 01:29:39,587

1986
01:29:42,033 --> 01:29:42,324

1987
01:29:43,441 --> 01:29:43,702

1988
01:29:44,660 --> 01:29:44,904

1989
01:29:48,700 --> 01:29:48,988

1990
01:29:52,791 --> 01:29:53,055

1991
01:29:53,632 --> 01:29:53,932

1992
01:29:55,101 --> 01:29:55,376

1993
01:29:55,690 --> 01:29:55,940

1994
01:29:56,071 --> 01:29:56,306

1995
01:29:56,191 --> 01:29:56,390

1996
01:29:56,714 --> 01:29:56,918

1997
01:30:00,352 --> 01:30:00,575

1998
01:30:01,571 --> 01:30:01,857

1999
01:30:02,401 --> 01:30:02,640

2000
01:30:02,661 --> 01:30:02,907

2001
01:30:05,030 --> 01:30:05,320

2002
01:30:05,420 --> 01:30:05,675

2003
01:30:05,612 --> 01:30:05,853

2004
01:30:06,380 --> 01:30:06,672

2005
01:30:08,230 --> 01:30:08,467

2006
01:30:09,131 --> 01:30:09,533

2007
01:30:09,711 --> 01:30:09,915

2008
01:30:12,211 --> 01:30:12,415

2009
01:30:12,725 --> 01:30:13,010

2010
01:30:13,110 --> 01:30:13,329

2011
01:30:15,090 --> 01:30:15,366

2012
01:30:15,410 --> 01:30:15,651

2013
01:30:17,011 --> 01:30:17,284

2014
01:30:17,390 --> 01:30:17,674

2015
01:30:17,841 --> 01:30:18,113

2016
01:30:18,029 --> 01:30:18,318

2017
01:30:22,970 --> 01:30:23,180

2018
01:30:23,802 --> 01:30:24,040

2019
01:30:24,190 --> 01:30:24,473

2020
01:30:25,210 --> 01:30:25,451

2021
01:30:25,980 --> 01:30:26,256

2022
01:30:26,111 --> 01:30:26,346

2023
01:30:27,510 --> 01:30:27,753

2024
01:30:29,510 --> 01:30:29,766

2025
01:30:31,302 --> 01:30:31,507

2026
01:30:34,241 --> 01:30:34,515

2027
01:30:34,690 --> 01:30:34,974

2028
01:30:36,551 --> 01:30:36,761

2029
01:30:41,351 --> 01:30:41,584

2030
01:30:43,021 --> 01:30:43,263

2031
01:30:47,699 --> 01:30:47,972

2032
01:30:51,469 --> 01:30:51,750

2033
01:30:54,621 --> 01:30:54,857

2034
01:30:56,601 --> 01:30:56,889

2035
01:30:58,909 --> 01:30:59,197

2036
01:31:03,010 --> 01:31:03,247

2037
01:31:03,140 --> 01:31:03,397

2038
01:31:04,873 --> 01:31:05,147

2039
01:31:05,509 --> 01:31:05,758

2040
01:31:06,340 --> 01:31:06,629

2041
01:31:06,529 --> 01:31:06,792

2042
01:31:07,754 --> 01:31:08,032

2043
01:31:08,129 --> 01:31:08,398

2044
01:31:10,630 --> 01:31:10,889

2045
01:31:12,620 --> 01:31:12,863

2046
01:31:13,509 --> 01:31:13,744

2047
01:31:14,151 --> 01:31:14,405

2048
01:31:14,539 --> 01:31:14,793

2049
01:31:15,109 --> 01:31:15,378

2050
01:31:16,520 --> 01:31:16,796

2051
01:31:20,750 --> 01:31:21,003

2052
01:31:21,010 --> 01:31:21,275

2053
01:31:21,840 --> 01:31:22,089

2054
01:31:23,891 --> 01:31:24,146

2055
01:31:25,040 --> 01:31:25,300

2056
01:31:25,364 --> 01:31:25,607

2057
01:31:26,461 --> 01:31:26,689

2058
01:31:26,969 --> 01:31:27,256

2059
01:31:29,021 --> 01:31:29,233

2060
01:31:29,602 --> 01:31:29,884

2061
01:31:29,850 --> 01:31:30,075

2062
01:31:30,300 --> 01:31:30,586

2063
01:31:30,813 --> 01:31:31,047

2064
01:31:33,500 --> 01:31:33,743

2065
01:31:36,448 --> 01:31:36,739

2066
01:31:38,430 --> 01:31:38,714

2067
01:31:40,349 --> 01:31:40,592

2068
01:31:42,793 --> 01:31:43,037

2069
01:31:43,109 --> 01:31:43,444

2070
01:31:43,499 --> 01:31:43,734

2071
01:31:44,909 --> 01:31:45,120

2072
01:31:45,230 --> 01:31:45,500

2073
01:31:46,759 --> 01:31:46,992

2074
01:31:47,274 --> 01:31:47,495

2075
01:31:48,872 --> 01:31:49,097

2076
01:31:49,074 --> 01:31:49,349

2077
01:31:50,029 --> 01:31:50,251

2078
01:31:51,572 --> 01:31:51,777

2079
01:31:52,980 --> 01:31:53,243

2080
01:31:54,389 --> 01:31:54,618

2081
01:31:55,860 --> 01:31:56,140

2082
01:31:57,389 --> 01:31:57,618

2083
01:31:59,452 --> 01:31:59,744

2084
01:31:59,771 --> 01:32:00,006

2085
01:32:01,689 --> 01:32:01,908

2086
01:32:02,519 --> 01:32:02,789

2087
01:32:03,353 --> 01:32:03,582

2088
01:32:05,719 --> 01:32:05,990

2089
01:32:08,032 --> 01:32:08,290

2090
01:32:09,310 --> 01:32:09,532

2091
01:32:09,949 --> 01:32:10,176

2092
01:32:11,681 --> 01:32:11,957

2093
01:32:15,081 --> 01:32:15,308

2094
01:32:15,659 --> 01:32:15,944

2095
01:32:16,169 --> 01:32:16,455

2096
01:32:16,549 --> 01:32:16,781

2097
01:32:18,539 --> 01:32:18,766

2098
01:32:21,739 --> 01:32:22,025

2099
01:32:23,091 --> 01:32:23,298

2100
01:32:25,140 --> 01:32:25,431

2101
01:32:25,649 --> 01:32:25,913

2102
01:32:25,911 --> 01:32:26,191

2103
01:32:26,549 --> 01:32:26,837

2104
01:32:27,118 --> 01:32:27,342

2105
01:32:27,378 --> 01:32:27,616

2106
01:32:28,211 --> 01:32:28,493

2107
01:32:29,168 --> 01:32:29,446

2108
01:32:30,448 --> 01:32:30,714

2109
01:32:33,978 --> 01:32:34,250

2110
01:32:38,908 --> 01:32:39,191

2111
01:32:39,489 --> 01:32:39,705

2112
01:32:40,258 --> 01:32:40,502

2113
01:32:43,138 --> 01:32:43,379

2114
01:32:47,172 --> 01:32:47,431

2115
01:32:49,351 --> 01:32:49,571

2116
01:32:50,569 --> 01:32:50,825

2117
01:32:52,808 --> 01:32:53,081

2118
01:32:53,958 --> 01:32:54,240

2119
01:32:54,538 --> 01:32:54,772

2120
01:32:55,502 --> 01:32:55,724

2121
01:32:55,758 --> 01:32:56,001

2122
01:32:56,469 --> 01:32:56,712

2123
01:32:56,657 --> 01:32:56,928

2124
01:32:57,617 --> 01:32:57,904

2125
01:32:58,708 --> 01:32:58,963

2126
01:33:00,558 --> 01:33:00,826

2127
01:33:01,388 --> 01:33:01,639

2128
01:33:03,438 --> 01:33:03,700

2129
01:33:05,110 --> 01:33:05,373

2130
01:33:07,163 --> 01:33:07,432

2131
01:33:10,429 --> 01:33:10,711

2132
01:33:11,128 --> 01:33:11,407

2133
01:33:11,711 --> 01:33:11,926

2134
01:33:11,897 --> 01:33:12,128

2135
01:33:12,478 --> 01:33:12,765

2136
01:33:12,798 --> 01:33:13,067

2137
01:33:13,311 --> 01:33:13,540

2138
01:33:13,569 --> 01:33:13,868

2139
01:33:13,948 --> 01:33:14,175

2140
01:33:14,338 --> 01:33:14,630

2141
01:33:15,488 --> 01:33:15,743

2142
01:33:17,792 --> 01:33:18,057

2143
01:33:21,000 --> 01:33:21,241

2144
01:33:21,773 --> 01:33:21,987

2145
01:33:23,558 --> 01:33:23,825

2146
01:33:24,389 --> 01:33:24,682

2147
01:33:24,708 --> 01:33:24,980

2148
01:33:25,547 --> 01:33:25,810

2149
01:33:28,878 --> 01:33:29,141

2150
01:33:31,889 --> 01:33:32,105

2151
01:33:32,788 --> 01:33:33,068

2152
01:33:33,428 --> 01:33:33,688

2153
01:33:33,677 --> 01:33:33,906

2154
01:33:34,188 --> 01:33:34,411

2155
01:33:36,427 --> 01:33:36,852

2156
01:33:39,000 --> 01:33:39,250

2157
01:33:39,127 --> 01:33:39,378

2158
01:33:39,768 --> 01:33:40,010

2159
01:33:41,178 --> 01:33:41,469

2160
01:33:41,309 --> 01:33:41,545

2161
01:33:42,269 --> 01:33:42,546

2162
01:33:43,608 --> 01:33:43,907

2163
01:33:43,737 --> 01:33:43,981

2164
01:33:44,188 --> 01:33:44,389

2165
01:33:48,231 --> 01:33:48,508

2166
01:33:49,830 --> 01:33:50,108

2167
01:33:50,017 --> 01:33:50,446

2168
01:33:51,298 --> 01:33:51,573

2169
01:33:51,487 --> 01:33:51,739

2170
01:33:51,937 --> 01:33:52,175

2171
01:33:52,579 --> 01:33:52,808

2172
01:33:52,766 --> 01:33:52,986

2173
01:33:53,479 --> 01:33:53,762

2174
01:33:56,038 --> 01:33:56,255

2175
01:33:59,111 --> 01:33:59,345

2176
01:34:00,838 --> 01:34:01,090

2177
01:34:03,468 --> 01:34:03,686

2178
01:34:07,118 --> 01:34:07,342

2179
01:34:08,018 --> 01:34:08,308

2180
01:34:09,166 --> 01:34:09,455

2181
01:34:09,818 --> 01:34:10,047

2182
01:34:12,378 --> 01:34:12,623

2183
01:34:14,246 --> 01:34:14,466

2184
01:34:15,318 --> 01:34:15,587

2185
01:34:17,428 --> 01:34:17,720

2186
01:34:18,397 --> 01:34:18,646

2187
01:34:19,226 --> 01:34:19,458

2188
01:34:21,670 --> 01:34:21,912

2189
01:34:21,919 --> 01:34:22,191

2190
01:34:22,752 --> 01:34:22,992

2191
01:34:22,951 --> 01:34:23,361

2192
01:34:23,326 --> 01:34:23,584

2193
01:34:28,838 --> 01:34:29,100

2194
01:34:29,226 --> 01:34:29,519

2195
01:34:29,549 --> 01:34:29,765

2196
01:34:30,376 --> 01:34:30,668

2197
01:34:30,568 --> 01:34:30,880

2198
01:34:32,867 --> 01:34:33,095

2199
01:34:33,768 --> 01:34:34,024

2200
01:34:36,716 --> 01:34:37,014

2201
01:34:36,848 --> 01:34:37,072

2202
01:34:37,037 --> 01:34:37,284

2203
01:34:37,229 --> 01:34:37,431

2204
01:34:38,130 --> 01:34:38,364

2205
01:34:41,199 --> 01:34:41,435

2206
01:34:46,010 --> 01:34:46,249

2207
01:34:46,197 --> 01:34:46,464

2208
01:34:47,028 --> 01:34:47,275

2209
01:34:48,061 --> 01:34:48,339

2210
01:34:50,227 --> 01:34:50,433

2211
01:34:51,197 --> 01:34:51,473

2212
01:34:51,517 --> 01:34:51,749

2213
01:34:51,968 --> 01:34:52,262

2214
01:34:52,354 --> 01:34:52,617

2215
01:34:52,666 --> 01:34:52,906

2216
01:34:54,078 --> 01:34:54,351

2217
01:34:55,167 --> 01:34:55,425

2218
01:34:58,108 --> 01:34:58,354

2219
01:35:00,548 --> 01:35:00,808

2220
01:35:00,810 --> 01:35:01,058

2221
01:35:01,069 --> 01:35:01,345

2222
01:35:01,388 --> 01:35:01,657

2223
01:35:01,706 --> 01:35:01,990

2224
01:35:02,026 --> 01:35:02,246

2225
01:35:03,829 --> 01:35:04,083

2226
01:35:04,708 --> 01:35:04,987

2227
01:35:08,176 --> 01:35:08,467

2228
01:35:08,306 --> 01:35:08,532

2229
01:35:10,097 --> 01:35:10,363

2230
01:35:11,568 --> 01:35:11,778

2231
01:35:12,656 --> 01:35:12,927

2232
01:35:12,786 --> 01:35:13,018

2233
01:35:14,507 --> 01:35:14,746

2234
01:35:16,438 --> 01:35:16,703

2235
01:35:21,306 --> 01:35:21,527

2236
01:35:25,787 --> 01:35:26,108

2237
01:35:27,136 --> 01:35:27,395

2238
01:35:27,386 --> 01:35:27,672

2239
01:35:31,747 --> 01:35:32,008

2240
01:35:31,946 --> 01:35:32,186

2241
01:35:32,908 --> 01:35:33,144

2242
01:35:35,145 --> 01:35:35,383

2243
01:35:35,586 --> 01:35:35,853

2244
01:35:39,309 --> 01:35:39,607

2245
01:35:42,067 --> 01:35:42,352

2246
01:35:44,747 --> 01:35:44,987

2247
01:35:45,388 --> 01:35:45,649

2248
01:35:46,739 --> 01:35:46,988

2249
01:35:48,346 --> 01:35:48,619

2250
01:35:50,967 --> 01:35:51,244

2251
01:35:52,377 --> 01:35:52,656

2252
01:35:52,696 --> 01:35:52,913

2253
01:35:55,709 --> 01:35:55,918

2254
01:35:58,469 --> 01:35:58,732

2255
01:36:02,557 --> 01:36:02,798

2256
01:36:03,067 --> 01:36:03,294

2257
01:36:03,836 --> 01:36:04,103

2258
01:36:04,025 --> 01:36:04,285

2259
01:36:06,725 --> 01:36:06,998

2260
01:36:06,856 --> 01:36:07,102

2261
01:36:07,105 --> 01:36:07,342

2262
01:36:08,136 --> 01:36:08,418

2263
01:36:10,129 --> 01:36:10,408

2264
01:36:11,466 --> 01:36:11,726

2265
01:36:16,335 --> 01:36:16,596

2266
01:36:16,904 --> 01:36:17,123

2267
01:36:18,129 --> 01:36:18,364

2268
01:36:19,985 --> 01:36:20,191

2269
01:36:23,314 --> 01:36:23,602

2270
01:36:26,196 --> 01:36:26,424

2271
01:36:26,515 --> 01:36:26,787

2272
01:36:30,686 --> 01:36:30,947

2273
01:36:31,265 --> 01:36:31,541

2274
01:36:31,458 --> 01:36:31,694

2275
01:36:32,545 --> 01:36:32,834

2276
01:36:33,376 --> 01:36:33,597

2277
01:36:37,666 --> 01:36:37,933

2278
01:36:37,865 --> 01:36:38,103

2279
01:36:38,376 --> 01:36:38,648

2280
01:36:40,544 --> 01:36:40,747

2281
01:36:42,918 --> 01:36:43,135

2282
01:36:43,556 --> 01:36:43,772

2283
01:36:44,197 --> 01:36:44,435

2284
01:36:44,967 --> 01:36:45,195

2285
01:36:47,026 --> 01:36:47,282

2286
01:36:47,274 --> 01:36:47,545

2287
01:36:49,585 --> 01:36:49,831

2288
01:36:50,100 --> 01:36:50,376

2289
01:36:50,925 --> 01:36:51,197

2290
01:36:52,147 --> 01:36:52,431

2291
01:36:53,556 --> 01:36:53,803

2292
01:36:54,136 --> 01:36:54,415

2293
01:36:55,926 --> 01:36:56,210

2294
01:36:56,054 --> 01:36:56,298

2295
01:37:04,385 --> 01:37:04,609

2296
01:37:06,178 --> 01:37:06,468

2297
01:37:06,365 --> 01:37:06,592

2298
01:37:07,328 --> 01:37:07,577

2299
01:37:07,965 --> 01:37:08,209

2300
01:37:08,155 --> 01:37:08,419

2301
01:37:08,346 --> 01:37:08,635

2302
01:37:08,546 --> 01:37:08,795

2303
01:37:08,734 --> 01:37:08,979

2304
01:37:09,505 --> 01:37:09,777

2305
01:37:09,627 --> 01:37:09,863

2306
01:37:15,976 --> 01:37:16,253

2307
01:37:16,808 --> 01:37:17,020

2308
01:37:16,935 --> 01:37:17,192

2309
01:37:20,714 --> 01:37:20,940

2310
01:37:20,907 --> 01:37:21,125

2311
01:37:22,575 --> 01:37:22,828

2312
01:37:23,536 --> 01:37:23,823

2313
01:37:26,424 --> 01:37:26,735

2314
01:37:26,938 --> 01:37:27,187

2315
01:37:27,190 --> 01:37:27,422

2316
01:37:29,815 --> 01:37:30,055

2317
01:37:29,946 --> 01:37:30,166

2318
01:37:34,626 --> 01:37:34,882

2319
01:37:37,825 --> 01:37:38,104

2320
01:37:38,205 --> 01:37:38,487

2321
01:37:39,867 --> 01:37:40,114

2322
01:37:40,386 --> 01:37:40,678

2323
01:37:43,335 --> 01:37:43,620

2324
01:37:44,167 --> 01:37:44,400

2325
01:37:46,347 --> 01:37:46,581

2326
01:37:50,116 --> 01:37:50,375

2327
01:37:50,898 --> 01:37:51,210

2328
01:37:51,404 --> 01:37:51,733

2329
01:37:51,726 --> 01:37:52,024

2330
01:37:52,045 --> 01:37:52,277

2331
01:37:52,234 --> 01:37:52,451

2332
01:37:55,307 --> 01:37:55,553

2333
01:37:57,614 --> 01:37:57,871

2334
01:38:02,613 --> 01:38:02,848

2335
01:38:06,065 --> 01:38:06,283

2336
01:38:07,746 --> 01:38:08,004

2337
01:38:08,506 --> 01:38:08,726

2338
01:38:09,027 --> 01:38:09,252

2339
01:38:10,307 --> 01:38:10,529

2340
01:38:10,555 --> 01:38:10,810

2341
01:38:11,514 --> 01:38:11,805

2342
01:38:11,837 --> 01:38:12,131

2343
01:38:12,474 --> 01:38:12,758

2344
01:38:13,506 --> 01:38:13,788

2345
01:38:13,887 --> 01:38:14,163

2346
01:38:15,106 --> 01:38:15,388

2347
01:38:17,547 --> 01:38:17,834

2348
01:38:18,887 --> 01:38:19,174

2349
01:38:19,719 --> 01:38:19,953

2350
01:38:21,315 --> 01:38:21,541

2351
01:38:22,215 --> 01:38:22,501

2352
01:38:22,347 --> 01:38:22,579

2353
01:38:24,269 --> 01:38:24,539

2354
01:38:24,591 --> 01:38:24,814

2355
01:38:26,504 --> 01:38:26,729

2356
01:38:28,750 --> 01:38:28,958

2357
01:38:29,643 --> 01:38:29,916

2358
01:38:34,324 --> 01:38:34,530

2359
01:38:35,473 --> 01:38:35,684

2360
01:38:36,184 --> 01:38:36,405

2361
01:38:38,934 --> 01:38:39,191

2362
01:38:40,415 --> 01:38:40,669

2363
01:38:41,058 --> 01:38:41,292

2364
01:38:41,627 --> 01:38:41,902

2365
01:38:43,676 --> 01:38:43,968

2366
01:38:44,064 --> 01:38:44,321

2367
01:38:45,596 --> 01:38:45,818

2368
01:38:45,853 --> 01:38:46,085

2369
01:38:47,964 --> 01:38:48,224

2370
01:38:48,295 --> 01:38:48,580

2371
01:38:49,183 --> 01:38:49,469

2372
01:38:52,834 --> 01:38:53,056

2373
01:38:54,307 --> 01:38:54,580

2374
01:38:54,944 --> 01:38:55,285

2375
01:38:57,906 --> 01:38:58,119

2376
01:39:00,267 --> 01:39:00,559

2377
01:39:00,713 --> 01:39:00,989

2378
01:39:02,637 --> 01:39:02,891

2379
01:39:03,537 --> 01:39:03,770

2380
01:39:04,175 --> 01:39:04,419

2381
01:39:04,889 --> 01:39:05,164

2382
01:39:05,263 --> 01:39:05,548

2383
01:39:06,163 --> 01:39:06,445

2384
01:39:09,044 --> 01:39:09,315

2385
01:39:09,493 --> 01:39:09,924

2386
01:39:10,966 --> 01:39:12,273

2387
01:39:11,734 --> 01:39:12,021

2388
01:39:14,493 --> 01:39:14,793

2389
01:39:15,773 --> 01:39:16,067

2390
01:39:16,094 --> 01:39:16,472

2391
01:39:18,465 --> 01:39:18,731

2392
01:39:19,616 --> 01:39:19,895

2393
01:39:19,803 --> 01:39:20,020

2394
01:39:20,634 --> 01:39:20,878

2395
01:39:24,484 --> 01:39:24,706

2396
01:39:26,274 --> 01:39:26,511

2397
01:39:26,664 --> 01:39:26,925

2398
01:39:28,196 --> 01:39:28,399

2399
01:39:30,383 --> 01:39:30,671

2400
01:39:31,913 --> 01:39:32,195

2401
01:39:33,194 --> 01:39:33,458

2402
01:39:33,903 --> 01:39:34,123

2403
01:39:34,794 --> 01:39:35,081

2404
01:39:35,945 --> 01:39:36,219

2405
01:39:36,264 --> 01:39:36,493

2406
01:39:37,874 --> 01:39:38,096

2407
01:39:38,582 --> 01:39:38,814

2408
01:39:38,833 --> 01:39:39,085

2409
01:39:39,344 --> 01:39:39,565

2410
01:39:40,693 --> 01:39:41,009

2411
01:39:43,125 --> 01:39:43,373

2412
01:39:44,985 --> 01:39:45,270

2413
01:39:46,393 --> 01:39:46,623

2414
01:39:46,584 --> 01:39:46,789

2415
01:39:47,224 --> 01:39:47,497

2416
01:39:47,743 --> 01:39:47,963

2417
01:39:48,254 --> 01:39:48,626

2418
01:39:49,534 --> 01:39:49,759

2419
01:39:51,644 --> 01:39:51,851

2420
01:39:56,005 --> 01:39:56,262

2421
01:40:03,053 --> 01:40:03,302

2422
01:40:03,943 --> 01:40:04,168

2423
01:40:05,672 --> 01:40:05,920

2424
01:40:08,233 --> 01:40:08,532

2425
01:40:11,572 --> 01:40:11,849

2426
01:40:11,896 --> 01:40:12,187

2427
01:40:12,402 --> 01:40:12,627

2428
01:40:13,103 --> 01:40:13,365

2429
01:40:14,064 --> 01:40:14,284

2430
01:40:18,745 --> 01:40:18,976

2431
01:40:18,874 --> 01:40:19,179

2432
01:40:19,513 --> 01:40:19,762

2433
01:40:19,704 --> 01:40:19,945

2434
01:40:21,243 --> 01:40:21,514

2435
01:40:24,827 --> 01:40:25,067

2436
01:40:26,044 --> 01:40:26,295

2437
01:40:26,302 --> 01:40:26,551

2438
01:40:26,943 --> 01:40:27,200

2439
01:40:28,104 --> 01:40:28,358

2440
01:40:28,743 --> 01:40:28,965

2441
01:40:28,992 --> 01:40:29,269

2442
01:40:29,824 --> 01:40:30,105

2443
01:40:31,108 --> 01:40:31,386

2444
01:40:32,263 --> 01:40:32,560

2445
01:40:33,793 --> 01:40:34,046

2446
01:40:36,308 --> 01:40:36,539

2447
01:40:38,413 --> 01:40:38,679

2448
01:40:39,886 --> 01:40:40,160

2449
01:40:41,485 --> 01:40:41,706

2450
01:40:45,072 --> 01:40:45,350

2451
01:40:48,024 --> 01:40:48,344

2452
01:40:50,452 --> 01:40:50,765

2453
01:40:50,833 --> 01:40:51,062

2454
01:40:50,964 --> 01:40:51,785

2455
01:40:51,933 --> 01:40:52,179

2456
01:40:52,183 --> 01:40:52,434

2457
01:40:52,891 --> 01:40:53,114

2458
01:40:54,233 --> 01:40:54,454

2459
01:40:54,742 --> 01:40:55,012

2460
01:40:54,871 --> 01:40:55,118

2461
01:40:55,903 --> 01:40:56,171

2462
01:40:56,221 --> 01:40:56,438

2463
01:40:56,415 --> 01:40:56,679

2464
01:40:56,864 --> 01:40:57,076

2465
01:40:57,242 --> 01:40:57,513

2466
01:40:57,883 --> 01:40:58,112

2467
01:40:58,464 --> 01:40:58,727

2468
01:40:58,782 --> 01:40:59,016

2469
01:40:59,683 --> 01:40:59,933

2470
01:41:06,276 --> 01:41:06,567

2471
01:41:07,102 --> 01:41:07,392

2472
01:41:08,264 --> 01:41:08,540

2473
01:41:09,804 --> 01:41:10,004

2474
01:41:10,762 --> 01:41:11,010

2475
01:41:11,663 --> 01:41:11,920

2476
01:41:11,982 --> 01:41:12,218

2477
01:41:12,426 --> 01:41:12,703

2478
01:41:13,193 --> 01:41:13,448

2479
01:41:14,151 --> 01:41:14,417

2480
01:41:16,403 --> 01:41:16,624

2481
01:41:16,662 --> 01:41:16,909

2482
01:41:17,042 --> 01:41:17,310

2483
01:41:17,361 --> 01:41:17,583

2484
01:41:17,625 --> 01:41:17,919

2485
01:41:18,324 --> 01:41:18,574

2486
01:41:20,242 --> 01:41:20,519

2487
01:41:21,263 --> 01:41:21,473

2488
01:41:22,422 --> 01:41:22,673

2489
01:41:23,441 --> 01:41:23,720

2490
01:41:23,572 --> 01:41:23,788

2491
01:41:27,482 --> 01:41:27,745

2492
01:41:27,932 --> 01:41:28,225

2493
01:41:28,503 --> 01:41:29,062

2494
01:41:30,236 --> 01:41:30,527

2495
01:41:30,421 --> 01:41:30,901

2496
01:41:30,942 --> 01:41:31,225

2497
01:41:32,022 --> 01:41:32,289

2498
01:41:34,402 --> 01:41:34,666

2499
01:41:35,171 --> 01:41:35,403

2500
01:41:38,622 --> 01:41:38,896

2501
01:41:41,384 --> 01:41:41,638

2502
01:41:41,832 --> 01:41:42,072

2503
01:41:42,922 --> 01:41:43,206

2504
01:41:43,502 --> 01:41:43,713

2505
01:41:51,701 --> 01:41:51,981

2506
01:41:51,951 --> 01:41:52,216

2507
01:41:52,345 --> 01:41:52,558

2508
01:41:53,232 --> 01:41:53,481

2509
01:41:59,323 --> 01:41:59,547

2510
01:42:01,827 --> 01:42:02,076

2511
01:42:04,893 --> 01:42:05,186

2512
01:42:05,025 --> 01:42:05,259

2513
01:42:06,303 --> 01:42:06,581

2514
01:42:07,073 --> 01:42:07,302

2515
01:42:07,842 --> 01:42:08,059

2516
01:42:09,312 --> 01:42:09,579

2517
01:42:09,822 --> 01:42:10,085

2518
01:42:10,141 --> 01:42:10,431

2519
01:42:10,912 --> 01:42:11,122

2520
01:42:12,961 --> 01:42:13,231

2521
01:42:19,885 --> 01:42:20,141

2522
01:42:20,071 --> 01:42:20,360

2523
01:42:21,102 --> 01:42:21,312

2524
01:42:23,471 --> 01:42:23,723

2525
01:42:25,904 --> 01:42:26,127

2526
01:42:30,902 --> 01:42:31,139

2527
01:42:32,631 --> 01:42:32,902

2528
01:42:33,590 --> 01:42:33,835

2529
01:42:33,921 --> 01:42:34,166

2530
01:42:34,813 --> 01:42:35,100

2531
01:42:36,221 --> 01:42:36,464

2532
01:42:40,000 --> 01:42:40,244

2533
01:42:40,265 --> 01:42:40,474

2534
01:42:40,511 --> 01:42:40,741

2535
01:42:41,345 --> 01:42:41,595

2536
01:42:42,695 --> 01:42:42,968

2537
01:42:44,101 --> 01:42:44,374

2538
01:42:44,221 --> 01:42:44,495

2539
01:42:44,742 --> 01:42:45,022

2540
01:42:47,243 --> 01:42:47,495

2541
01:42:48,331 --> 01:42:48,589

2542
01:42:48,781 --> 01:42:49,054

2543
01:42:49,350 --> 01:42:49,592

2544
01:42:49,801 --> 01:42:50,044

2545
01:42:58,640 --> 01:42:58,877

2546
01:42:59,152 --> 01:42:59,405

2547
01:42:59,541 --> 01:42:59,784

2548
01:43:00,051 --> 01:43:00,338

2549
01:43:00,181 --> 01:43:00,429

2550
01:43:00,754 --> 01:43:01,035

2551
01:43:05,056 --> 01:43:05,343

2552
01:43:05,241 --> 01:43:05,516

2553
01:43:06,711 --> 01:43:06,921

2554
01:43:10,302 --> 01:43:10,581

2555
01:43:10,490 --> 01:43:10,772

2556
01:43:12,860 --> 01:43:13,053

2557
01:43:14,401 --> 01:43:14,688

2558
01:43:14,591 --> 01:43:14,802

2559
01:43:17,663 --> 01:43:17,937

2560
01:43:20,040 --> 01:43:20,307

2561
01:43:21,770 --> 01:43:22,030

2562
01:43:23,051 --> 01:43:23,336

2563
01:43:25,031 --> 01:43:25,299

2564
01:43:25,804 --> 01:43:26,093

2565
01:43:27,862 --> 01:43:28,072