Re: [微積] 2題無窮級數和
※ 引述《KitWoolsey (難得好天氣)》之銘言：
: 1 sigma(1~無窮大) x.e^(-x^2) = ?
: 2 sigma(1~無窮大) 1/(x+x^3) = ?
: 3 sigma(1~無窮大) 1/(xlnx) = ? 竟然沒發現 還想半天 = =
: 有些看起來好像某些函數的微分/積分型 可是微分積分一下也看不出來個所以然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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