How to calculate the Laurent series expansion of 1/(1-z)² in the region 1<|z|?

[Eldonbetan]

1. I am trying to calculate the laurent series expansion of the function 1/(1-z)² in the region 1<|z|


2. None


3. I can get an answer informally by doing the polynomial division like in high school, but I don't know if this is the right answer and in case it is I cannot prove it. Any help would be largely appreciated.

 

[hgfalling]

Recall that if a function is analytic on a domain, then its Laurent series and Taylor series are identical. Do you know how to do the Taylor series expansion?