(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to find the sum of a given infinite series when [itex]|x|<1[/itex] (which is the radius of this series)

2. Relevant equations

[itex]\sum_{n=1}^{∞}(-1)^{n+1}\frac{x^{2n+1}}{4n^2-1} [/itex]

3. The attempt at a solution

I've tried to do the following:

[itex]S'(x) = \sum_{n=1}^{∞}(-1)^{n+1}\frac{x^{2n}}{2n-1} \\

S''(x) = \sum_{n=1}^{∞}(-1)^{n+1}\frac{2nx^{2n-1}}{2n-1}\\

S'''(x) = 2\sum_{n=1}^{∞}(-1)^{n+1}nx^{2(n-1)}\\[/itex]

And I was thinking about substitution [itex]t = x^2[/itex], but I had no success.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sum of infinite series

**Physics Forums | Science Articles, Homework Help, Discussion**