# power series sum-function!

• May 29th 2013, 06:34 AM
lawochekel
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
• May 29th 2013, 07:50 AM
JJacquelin
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.
• May 29th 2013, 01:35 PM
HallsofIvy
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?