题目

关于数学极限 天才 come here
lim(n^2(m/n-1/(n+1)-1/(n+2)-……-1/(n+m)))的值是多少 讲述一下思路
n→∞

提问时间：2020-11-15

答案

m/n-1/(n+1)-1/(n+2)-……-1/(n+m)
=[1/n-1/(n+1)]+[1/n-1/(n+2)]+.+[1/n-1/(n+m)]
=1/[n(n+1)]+2/[n(n+2)]+...+m/[n(n+m)]
所以当n→∞时
lim(n^2(m/n-1/(n+1)-1/(n+2)-……-1/(n+m)))
=lim{n^2/[n(n+1)]+2n^2/[n(n+2)]+...+m×n^2/[n(n+m)]}
=1+2+...+m