求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n
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![求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n](/uploads/image/z/3936035-11-5.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90+lim+n%5B1%2F%28n%5E2%2B1%29%2B1%2F%28n%5E2%2B2%5E2%EF%BC%89%2B%E2%80%A6%E2%80%A6%2B1%2F%28n%5En%2Bn%5En%29%5D+%28n%E8%B6%8B%E5%90%91%E4%BA%8E%E6%97%A0%E7%A9%B7%E5%A4%A7%2Cn%5En%E8%A1%A8%E7%A4%BAn)
求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n
求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n
求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n
=lim n^2·[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] /n
=lim [n^2/(n^2+1)+n^2/(n^2+2^2)+……+n^2/(n^n+n^n)]·(1/n)
=lim [1/(1+(1/n)^2) +1/(1+(2/n)^2) +……+ 1/(1+(n/n)^2))]·(1/n)
=∫《x从0到1》1/(1+x²) dx
=arctanx |《x从0到1》
=arctan1 - arctan0
=π/4
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