F.6 Power Series

👨🏻‍🏫 學術台數學

用戶11165

2011-05-07 9:16 pm

I was able to find the radius of convergence
but I got stuck when I am going to substitute the endpoints to the series

圖片參考：http://imgcld.yimg.com/8/n/HA00008075/o/701105070046913873435080.jpg

thanks a lot.......

更新1:

The answer is supposed to be in this form (-a, a) I know the radius of convergence but I don't know if the series converges when I plug -a and a into the power series that's why I create this question thanks a lot.....

更新2:

For 第二個回答: 我唔係質疑你個答案, 但係個series係alternating, sub -1/sqrt(2) 入去係divergent, 呢個小弟絕對理解咁到sub 1/sqrt(2) 入去果陣唔係可以用alternating series test 來prove到佢係convergent架咩?? 唔該哂

回答 (2)

act_2_mon

2011-05-08 7:01 am

✔ 最佳答案

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圖片參考：http://www.upload-jpg.com/images.php/4430c1754/Series.jpg

2011-05-07 23:15:43 補充：
上面唔識, 唔好亂答教錯人...

2011-05-08 09:27:15 補充：
你岩...我唔記得有(-1)^n係度....
so, it is ( -1/sr(2) 1/sr(2) ]

2011-05-08 09:34:20 補充：
哎呀...even -1/sr(2) converges too..
there's still a (-1)^n-1 in front..
so alternating series again..

2011-05-08 09:38:14 補充：
^ (-1)^n+1

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用戶25975

2011-05-08 9:19 pm

To act_2_mon:

我無亂答, 只係差左 forget to take limit n tends to infinity

唔該你睇清楚我 D record and 分清黑白, 別做高分低能.

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