已知數列a(n)=1/[n(n+1)], n=1,2,3,..., 試求
(1) Σ[n=1~∞] a(n) =?
(2) Σ[n=1~∞] [a(n)]^2 =?
(3) Σ[n=1~∞] [a(n)]^3 =?
無窮級數求值(3題)
2009-07-14 12:38 am
回答 (4)
2009-07-14 1:37 am
✔ 最佳答案
要用到 Σ[n=1~∞] 1/n^2 = π^2/62009-07-13 17:37:45 補充：
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參考: Myself
2009-07-14 12:57 am
可以求得closed form.
2009-07-14 12:55 am
需要用到Riemann zeta function嗎?
2009-07-14 1:08 am
用partial fraction也不是想像中般容易...
收錄日期: 2021-04-19 14:56:36
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090713000015KK07747