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In our algorithms class, my professor insists that n! Has a higher order of growth than n^n. 法二（错位相减）： 考虑幂级数 ∑ n = 1 ∞ n x n (1 x) ∑ n = 1 ∞ n x n = ∑ n = 1 ∞ n x n ∑ n = 1 ∞ n x n + 1 = x + ∑ n = 1 ∞ (n + 1) x n + 1 ∑ n = 1 ∞ n x n + 1 = x + ∑ n = 1 ∞ x n +.
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You'll need to complete a few actions and gain 15 reputation points before being able to upvote. This doesn't make sense to me, when i work through what each expression means. I'm trying to find $$\\lim_{n\\to\\infty}\\frac{n}{\\sqrt[n]{n!}}.$$ i tried couple of methods:
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请问一下e^ (n)*n!/n^ (n)这个极限为无穷大是怎么证明出来的？ [图片] [图片] 上课的时候，老师讲stirling公式时提到过这俩极限，第一个是正无穷，第二个是0，而当分母是n^ (n+1/2)的时候极.
Upvoting indicates when questions and answers are useful. To gain full voting privileges, $$ \\lim_{n \\to \\infty} n x^{n} = 0$$
