求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷
问题描述：
求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷
答
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*[(1/n(n+1))+(2/n(n+2))+……+(k/n(n+k))]=lim (n^2/n(n+1))+(2n^2/n(n+2))+……+(kn^2/n(...