Math Help - Power Series

1. Power Series

Find a power series representation for the function and determine the raidus of convergence.

f(x) = x^2/(1-2x)^2

Im having trouble isolating it to 1/1-x.

Anyone who can hint me something would be greatly appreciated. You do not need to solve it, please help me simplify it to 1/1-x. Thanks.

2. Re: Power Series

Try using the fact that $\dfrac{d}{dx}\left ( \dfrac{1}{1-x}\right ) = \dfrac{1}{(1-x)^2}$ to obtain the series for $\dfrac{1}{(1-x)^2}$ from $\dfrac{1}{1-x} = 1 + x + x^2 + \cdots$ and proceed from there.

--Kevin C.

3. f(x) = x^2/(1-2x)^2

what I do with the 2x?

4. Re: Power Series

If you have a series for $\dfrac{1}{(1-u)^2}$, then just subtitute $u=2x$ to get a series for $\dfrac{1}{(1-2x)^2}$ and proceed from there.

--Kevin C.