作者cxzdsa5566 (cxzdsa5566)
看板Math
标题Re: [微积] 2题无穷级数和
时间Wed Mar 23 02:20:30 2011
※ 引述《KitWoolsey (难得好天气)》之铭言：
: 1 sigma(1~无穷大) x.e^(-x^2) = ?
: 2 sigma(1~无穷大) 1/(x+x^3) = ?
: 3 sigma(1~无穷大) 1/(xlnx) = ? 竟然没发现 还想半天 = =
: 有些看起来好像某些函数的微分/积分型 可是微分积分一下也看不出来个所以然qq
1. Sx*e^(-x^2)dx = (-1/2)Se^(u)du (u=-x^2) =(-1/2) e(-x^2) from 1 to infinity
=1/(2e)
By Intergal Test, the series converges.
2. 1/(x+x^3)=1/[(x)(1+x^2)] = [1/x-x/(1+x^2)]
S[1/x-x/(1+x^2)]dx= ln|x/sqrt(1+x^2)| from 1 to infinity
=ln(sqrt(2))
By Integral Test, the series converges.
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◆ From: 140.112.218.123
1F：→ cxzdsa5566 :应该是这样吧@@?有点忘记了。 03/23 02:21
2F：推 a016258 :他并没有问敛散阿...他是问等於多少... 03/23 02:22
3F：→ KitWoolsey :感谢您的解答 但是我是要求值不是判断敛散啊..qq 03/23 09:48