# Math Help - power series sum-function!

1. ## power series sum-function!

i have a power series of this form

$\sum_{n=1}^{\infty} \frac{(-1)^nx^n}{n}$

on attempting, i arrived at the sum-function

$\frac{x}{n(1+x)}$

pls help if i missed it.

thanks

2. ## Re: power series sum-function!

The result MUST NOT contain n, because n is the variable index for sumation.
Derive the sum in order to get a geometric sum.
After expressing the geometric sum as a closed form, integrate it.

3. ## Re: power series sum-function!

Your sum is the same as $\sum_{n= 1}^\infty \frac{(-x)^n}{n}$.

Do you know the Taylor series for ln(x+ 1) about x= 0?