Hi,

I was trying to find a power series for function $\displaystyle ln((1+x)/(1-x))$.

I separated this into $\displaystyle ln(1+x)-ln(1-x)$ and used differentiation & integration to get $\displaystyle \sum_{n=0}^\infty\frac{(-1)^n(x)^{n+1}}{n+1} + \sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

The answer says $\displaystyle \sum_{n=0}^\infty\frac{2x^{2n+1}}{2n+1}$. I have no idea how this answer was derived. Can anyone explain to me how to get this answer?

Thanks!