作者yueayase (scrya)
看板Math
标题Re: [中学] 无穷级数
时间Tue May 15 23:52:29 2012
※ 引述《susiseptem (..)》之铭言：
: 无穷级数 1 至 无穷大 n(1/3)^n 之值
: 感谢板上专业的大大QQ
: 100P答谢
∞ n 2 3
令 F = Σ n(1/3) = 1/3 +2(1/3) + 3(1/3) + ....
n=1
同乘1/3
2 3
=>F/3 = (1/3) + 2(1/3) + .....
2 3 ∞ n 1/3
=> F-F/3 = 1/3 + (1/3) + (1/3) + ... = Σ (1/3) = ------- = 1/2
n=1 1-1/3
=> F = 3/4
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1F：推 susiseptem :谢谢大大 05/15 23:58