MHB Power series and uniform convergence.

MissC
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Hi.
I have this power serie (2^n/n)*z^n that runs from n=1 to infinity, and I have to show whether it's uniform konvergence on [-1/3, 1/3] or not.

I hope someone can help me with this.
 
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It is fairly standard to use the "ratio test" or "root test" to determine convergence of a power series. And I presume you know that "if a power series converges on a closed and bounded interval, then it converges uniformly there."
 
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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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