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 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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