# Homework Help: Coefficients of Series

1. Apr 13, 2010

### abc617

[PLAIN]http://img243.imageshack.us/img243/156/55139700.png [Broken]

Knowns
Well I know that
$$\sum \frac{1}{1-x}$$ = 1+$$x^{2}$$+$$x^{3}$$....

I know the integral is

[PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP32919a6dgiib73geda500000hd72bah4i062h1b?MSPStoreType=image/gif&s=36&w=241&h=38 [Broken]

I've first started with the known sum, then i replaced [x] with [PLAIN]http://www4c.wolframalpha.com/Calculate/MSP/MSP15219a6e2bf832h2gb6000039if18068de4ia05?MSPStoreType=image/gif&s=55&w=20&h=39 [Broken]

$$\sum \frac{1}{1-(x/2)^2}$$ = 1-(x^2/2)^2-(x^2/2)^3..

Then I tried to integrate the new sum [too long and latek is messing up for me] to get arctan. Then I multiplied it by 16.

I feel that i'm messing up somewhere, I just don't know where.

Last edited by a moderator: May 4, 2017
2. Apr 13, 2010

### sutupidmath

For the integral: In the denominator factor the 4, that is

$$\frac{16}{4((\frac{x}{2})^2+1)}$$

and use the hint.