我想請問,例如
∑{k=1,n}[(k+1)^2-1^2)=2^2-1^2+3^2-2^2+4^2-3^2+...+(n+1)^2-n^2
=(n+1)^2-1^2
中間d terms 全被 cancelled.
錦係咪叫difference method.如果唔係,叫咩?
Maths concept
2013-04-03 4:31 am
回答 (1)
2013-04-03 4:53 am
✔ 最佳答案
這種方法英文叫telescoping或method of difference。中文叫裂項求和。日文則叫畳み込み級数（たたみこみきゅうすう)例子∑ (n = 1 -> ∞) 1/[n(n + 1)]
= ∑ (n = 1 -> ∞) 1/n - 1/(n + 1)
= (1 - 1/2) + (1/2 - 1/3) + ... + (1/n - 1/(n + 1)) + ...
= 1
收錄日期: 2021-04-27 20:03:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130402000051KK00352