lim┬(n→∞)〖(1/(n^2+1)〗+2/(n^2+2)+⋯n/(n^2+n))等于1/2,
问题描述：
lim┬(n→∞)〖(1/(n^2+1)〗+2/(n^2+2)+⋯n/(n^2+n))等于1/2,
答
1/(n^2+1)+n/[n^2+n]=[(n^2+n)+n(n^2+1)]/[(n^2+1)(n^2+n)]=n^3/n^4*[1+1/n+2/n^2+1/n^3]/[(1+1/n^2)(1+1/n)]2/(n^2+2)+(n-1)/[n^2+n-1]=[2(n^2+n-1)+(n-1)(n^2+2)]/[(n^2+2)(n^2+n-1)]=n^3/n^4*[1+1/n+4/n^2+-4/n^3...