n(1/1+n^2+1/4+n^2+1/9+n^2+…+1/n^2+n^2)当n趋近于无穷大时怎么利用定积分求极限注意是利用定积分求极限
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 04:48:28
![n(1/1+n^2+1/4+n^2+1/9+n^2+…+1/n^2+n^2)当n趋近于无穷大时怎么利用定积分求极限注意是利用定积分求极限](/uploads/image/z/8855576-8-6.jpg?t=n%281%2F1%2Bn%5E2%2B1%2F4%2Bn%5E2%2B1%2F9%2Bn%5E2%2B%E2%80%A6%2B1%2Fn%5E2%2Bn%5E2%29%E5%BD%93n%E8%B6%8B%E8%BF%91%E4%BA%8E%E6%97%A0%E7%A9%B7%E5%A4%A7%E6%97%B6%E6%80%8E%E4%B9%88%E5%88%A9%E7%94%A8%E5%AE%9A%E7%A7%AF%E5%88%86%E6%B1%82%E6%9E%81%E9%99%90%E6%B3%A8%E6%84%8F%E6%98%AF%E5%88%A9%E7%94%A8%E5%AE%9A%E7%A7%AF%E5%88%86%E6%B1%82%E6%9E%81%E9%99%90)
n(1/1+n^2+1/4+n^2+1/9+n^2+…+1/n^2+n^2)当n趋近于无穷大时怎么利用定积分求极限注意是利用定积分求极限
n(1/1+n^2+1/4+n^2+1/9+n^2+…+1/n^2+n^2)当n趋近于无穷大时怎么利用定积分求极限
注意是利用定积分求极限
n(1/1+n^2+1/4+n^2+1/9+n^2+…+1/n^2+n^2)当n趋近于无穷大时怎么利用定积分求极限注意是利用定积分求极限
原式=
(n->∞)limn∑(i=1~n)1/(i^2+n^2)
=(n->∞)lim1/n∑(i=1~n)1/((i/n)^2+1)
=∫(0~1)1/(1+x^2)dx
=arctanx|(0,1)
=π/4