MHB Power series and uniform convergence.

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The discussion centers on determining the uniform convergence of the power series (2^n/n)*z^n over the interval [-1/3, 1/3]. The ratio test or root test is suggested as standard methods for assessing convergence. It is noted that if a power series converges on a closed and bounded interval, it also converges uniformly on that interval. Participants are encouraged to apply these tests to the given series. The conclusion emphasizes the importance of these tests in establishing 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'

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