i have a power series of this form

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

on attempting, i arrived at the sum-function

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

pls help if i missed it.

thanks

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- May 29th 2013, 06:34 AMlawochekelpower series sum-function!
i have a power series of this form

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

on attempting, i arrived at the sum-function

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

pls help if i missed it.

thanks - May 29th 2013, 07:50 AMJJacquelinRe: 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 PMHallsofIvyRe: power series sum-function!
Your sum is the same as $\displaystyle \sum_{n= 1}^\infty \frac{(-x)^n}{n}$.

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