计算lim n^2[(k/n - 1/(n+1) - 1/(n+2) - 1/(n+3)- … n→∞ 1/(n+k)]
热心网友
(nn)[k/n - 1/(n+1) - 1/(n+2) - 1/(n+3)-… -1/(n+k)]=(nn){[1/n-1/(n+1)]+[1/n-1/(n+2)]+[1/n-1/(n+3)]+…+[1/n-1/(n+k)]}=(nn)[1/(nn+n)+2/(nn+2n)+3/(nn+3n)+…+k/(nn+kn)]=1/(1+1/n)+2/(1+2/n)+3/(1+3/n)+…+k/(1+k/n)→1+2+3+…+k=[k(k+1)]/2(当n→∞时)。