Question

How do you find a power series representation for `f(x)=xln(x+1)` and what is the radius of convergence?

Answer 1

`x^2- x^3/2+x^4/3-...+(-1)^(n-1)x^n/n+..., -1 < x<=1`

Explanation:

Power series for `x ln(x+1)`

`=x`(power series for `ln(x+1)`

`=x(x-x^2/2+x^3/3-...), -1< x<=1`

`x^2-x^3/2+x^4/3-...+(-1)^(n-1)x^n/n+..., -1 < x<=1`