Quick complex analysis query

http://www.mathhelpforum.com/math-he...cons/icon1.gif **Quick complex analysis query**

Hi, I'm just working through examples for revision and I've come across one that I've worked but not sure if its correct. If anyone could check it would be much appreciated:

Expand 1/z in power series about z=1

Ok you can write 1/z as 1/[1+(z-1)] in this case since expansion is about 1. Then: 1/[1+(z-1)= 1/(1+(z-1)/1)=1[1-(z-1)+(z-1)^2-+....]

oo

=SUM (-1)^k(z-1)^k

k=0

Now is this sufficient for the question or have I left anything vitally important out. I am not great at the subject so I need to make sure anything I'm using as study exercises is working out correctly!

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