Limit
2010-01-23 7:52 am
回答 (1)
2010-01-23 9:31 am
✔ 最佳答案
Choose an integer M>|x|, so that |x|/M<1. For n>M, we have
0 <= |x|^n / n! = |x|^n / [1*2*...*M*(M+1)*...*n]
<= |x|^n / [M! M^{n-M}] = (M^M)/M! * (|x|/M)^n
Now since M^M/M! is a constant, and |x|/M<1,
by Sandwich Theorem, we have lim{n→∞} |x|^n/n! = 0
收錄日期: 2021-04-22 00:34:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100122000051KK01712