1道数列极限题计算limn^2(k/n-1/(n+1)-1/(n+2)-.-1/(n+k))1楼回答不正确无数个极限为0加起来不等于0

Question

1道数列极限题
计算 lim n^2(k/n-1/(n+1)-1/(n+2)-.-1/(n+k))
1楼回答不正确 无数个极限为0加起来不等于0

Answer 1

lim n^2(k/n-1/(n+1)-1/(n+2)-.-1/(n+k))
=lim n^2{[1/n-1/(n+1)]+[1/n-1/(n+2)].+[1/n-1/(n+k)]
=lim n^2/[n(n+1)]+n^2*2/[n(n+2)]+.+n^2*k/[n(n+k)]
=1+2+.k
=k*(k+1)/2