What is the sum to infinity of this nearly geometric series? • Physics Forums

Poirot1 · 2012-04-15T13:21:20+00:00

Find the sum to infinity of the series $1 +2z +3z^2+4z^3+...$

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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MHB What is the sum to infinity of this nearly geometric series?

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

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