Lim n-无穷大 n/(n^2+1^2)+n/(n^2+2^2)+.n/(n^2+n^2)
问题描述:
Lim n-无穷大 n/(n^2+1^2)+n/(n^2+2^2)+.n/(n^2+n^2)
答
lim(n趋近无穷){n/(n^2+1)+n/(n^2+2^2)+...+n/(n^2+n^2)}
=积分(x从0到1)1/(1+x^2)dx
=arctanx(x从0到1)
=pi/4.