Power series and uniform convergence.

[MissC]

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.

 

[HallsofIvy]

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."