Hey guys, I am having a bit of difficulty with this power series problem:

$\displaystyle \ln\sqrt\frac{1+2x}{1-2x}$

Basically I need to find a power series representation for this function. First I tried breaking this problem down through properties of logarithm:

$\displaystyle \frac{1}{2}[ln(1+2x) - ln(1-2x)]$

Then afterwards, I tried various steps and (random) methods to try and solve this problem. As of right now I am completely stuck, and I have no idea how to further continue this problem.

Any feedback and help on this problem would be greatly appreciated.

Thanks