# Power series representation of 10xarctan(5x).

1. Oct 9, 2007

### Boruedu

1. The problem statement, all variables and given/known data

The function f(x)=10xarctan(5x) is represented as a power series
http://img464.imageshack.us/img464/4131/formub5.jpg [Broken]
Find the first few(5) coefficients in the power series.

2. Relevant equations

I already know that the representation of arctanx is summation from n=0 to infinity of (-1)^n x^(2n+1)/(2n+1).

3. The attempt at a solution

So I plugged in 5x and then multiplied the entire thing by 10x.

I ended up with summation n=0 to infinity (-1)^n (10x)(5x)^2n+1/(2n+1) = 50x^2 + 10x(5x)^3/3-10x(5x)^5/5+...

I've asked a few people, and while they don't seem to remember power series very well, the only issue they could point out is that you can't multiply the whole thing by 10x. Is that true? If it is... then how do I go about solving this?

Last edited by a moderator: May 3, 2017
2. Oct 9, 2007

### Dick

Perhaps those few people remember even less than they thought. Because you certainly can do that.