关于数学极限天才 come herelim(n^2(m/n-1/(n+1)-1/(n+2)-……-1/(n+m)))的值是多少 _数学解答

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→∞

人气：219 ℃　时间：2020-02-03 13:46:30

解答

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