求[ n^2(k/n-1/(n+1)-1/(n+2)- .-1/(k+1)] 的极限的值
问题描述：
求[ n^2(k/n-1/(n+1)-1/(n+2)- .-1/(k+1)] 的极限的值
答
可以把k/n看作1/n+1/n+1/n.一共k个1/n（k*(1/n)）则原式=n^2(1/n-1/(n+1)+1/n-1/(n+2)+.+1/n-1/(k+1))=n^2(1/n(n-1)+2/n(n-1)+.+k/n(n-1))=n/(n-1)+2n/(n-1).kn/(n-1)lim[n/(n-1)+2n/(n-1).kn/(n-1)]=k(k+1)/2...