MHB Express $\frac{1}{z+1}$ as a power series about z=1

Poirot1
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express $\frac{1}{z+1}$ as a power series about z=1. My working: I know $\frac{1}{z+1}=1-z+z^2-z^3+...$ but this is macluarin series.
 
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Write $\frac 1{1+z}=\frac 1{2+(z-1)}=\frac 12\frac 1{1+\frac{z-1}2}$.
 

Thread 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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