lim┬(n→∞)⁡;〖(1/(n^2+1)〗+2/(n^2+2)+⋯;n/(n^2+n))等於1/2,

lim┬(n→∞)⁡;〖(1/(n^2+1)〗+2/(n^2+2)+⋯;n/(n^2+n))等於1/2,

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…