Trouble with an index change in Laurent series

[saybrook1]

Homework Statement

Hey guys, I'm just going through a Laurent series example and I'm having trouble understanding how they switched the index on a summation from n=0 to n=1 and then switched the argument from z^(-n-1) to z^n as well as changing the upper limit to -infinity. If anyone could shed some light on that for me I would really appreciate it.[/B]

Homework Equations

http://imgur.com/0PkgLim

The Attempt at a Solution

I thought that if you changed the index to n=1 then the power on z should just move up one erasing the ^(-1) and I'm not sure how switching the limit to negative infinity changes anything. Thanks for any help.

 

[vela]

Try rewriting the summation in terms of $k = -n-1$. What values does $k$ cover when $n$ goes from $0$ to $\infty$?

 

[saybrook1]

Thank you very much :)