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 '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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