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