Representation of Power Series Problem

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

Re: Representation of Power Series Problem

Have you tried using Maclaurin series for ln?

Re: Representation of Power Series Problem

First do the series for ln(1+u) about u = 0. Then plug in u=2x and u=-2x and subtract them. You'll get a lot of cancellation and simplification.

Re: Representation of Power Series Problem

Quote:

Originally Posted by

**emakarov**

Would you need to use the Mclaurin series for this. I just started learning about the Taylor/Mclaurin series, and this problem seems a bit complicated to use the Mclaurin series method.

Quote:

Originally Posted by

**johnsomeone** First do the series for ln(1+u) about u = 0. Then plug in u=2x and u=-2x and subtract them. You'll get a lot of cancellation and simplification.

Thanks! So basically, I can ignore the 1/2 (from the square root function) and just focus on the ln(1 + u) and simplify the problem, and then later factor in the 1/2?

Re: Representation of Power Series Problem

Mclaurin series is Taylor series about 0.

Quote:

Originally Posted by

**Beevo** Thanks! So basically, I can ignore the 1/2 (from the square root function) and just focus on the ln(1 + u) and simplify the problem, and then later factor in the 1/2?

Yes.