# Simple Power Series Question

• Feb 20th 2010, 03:55 PM
davismj
Simple Power Series Question

Is this sufficient for the question asked? or does that extra -1 make it less of a power series?

Thanks!
• Feb 20th 2010, 04:10 PM
Drexel28
Quote:

Originally Posted by davismj

Is this sufficient for the question asked? or does that extra -1 make it less of a power series?

Thanks!

I think you're missing a negative sign. $\displaystyle \frac{1+z}{1-z}=-\left(1+\frac{2}{1+z}\right)$...actually...two.
• Feb 20th 2010, 04:30 PM
davismj
Quote:

Originally Posted by Drexel28
I think you're missing a negative sign. $\displaystyle \frac{1+z}{1-z}=-\left(1+\frac{2}{1+z}\right)$...actually...two.

I'm sorry, but that doesn't really help (except I see my typo!)

From what I can tell, you've rewritten the original expression as

$\displaystyle \frac{1}{1-z} + \frac{z}{1-z}$ and of course $\displaystyle \frac{1}{1-z}$ is $\displaystyle \sum_{n=0}^{\infty}z^n$

Not sure where you're getting the negative sign from, though.