Power series representation of 10xarctan(5x).

[Boruedu]

Homework Statement

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

Homework Equations

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

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?

 

[Dick]

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