Question

一道关于幂级数展开的问题f(x)=(1/4)*ln[(1+x)/(1-x)]+(1/2)*arctanx-x展开成x的幂

Answer 1

f(x)=(1/4)*ln[(1+x)-ln(1-x)]+(1/2)*arctanx-x已知当|x|x] 1/(1+x^2) dx 当|x|x] 1-x^2+x^4-x^6+…… dx= x-x^3/3+x^5/5-x^7/7……=∑(-1)^n*x^(2n+1)/(2n+1) n from 0 to ∞所以f(x)=(1/4)*ln[(1+x)/(1-x)]+(1/2)*...