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!