作者smartlwj (要准备资格考)
看板trans_math
标题Re: [考古] 94年北科转学考
时间Thu Dec 2 12:27:02 2010
※ 引述《kensite702 (读书人)》之铭言：
: lim n
: ----------------
: x->∞ (n!)^1/n
题目应该是 n→∞
n!
Let f(n) = (-------)^(1/n)
n^n
1 1 n n 1 i
=> log f(n) = ---( log --- + ... + log ---) = Σ ---(log ---)
n n n i=1 n n
1 1 1
=>∫ log x dx = xlogx | - ∫ dx = -1
0 0 0
i.e. lim log f(n) = -1
n→∞
1
=> log lim f(n) = -1 => lim f(n) = ---
n→∞ n→∞ e
n
therefore, lim ---------- = e
n→∞(n!)^(1/n)
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不知道有没有算错...有错请指正
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