STEVIE-G™ 發問於 科學及數學數學 · 1 十年前

Limit

圖片參考:http://imgcld.yimg.com/8/n/HA00266150/o/7010012201...

Why??????Please explain!

1 個解答

評分
  • Jacob
    Lv 6
    1 十年前
    最愛解答

    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

還有問題嗎?立即提問即可得到解答。