作者keith291 (keith)
看板trans_math
标题Re: [微分] 一题证明
时间Tue Feb 9 16:52:44 2010
※ 引述《BIEGABOY (BIEGABOY)》之铭言：
: Let the sequence an=(1+1/n)^n
: 1.show that an is increasing.
即证
(1+1/n)^n < (1+1/(n+1))^(n+1)
pf:
由算几不等式:
共n个
╭────────────╮
(1+1/n)+(1+1/n)+....+(1+1/n) + 1 n+1
--------------------------------- > √((1+1/n)^n)
n+1
=> (1+1/(n+1))^(n+1) > (1+1/n)^n , Q.E.D.
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