Hello,

I have to find the radius of convergence with this series

$\displaystyle \Sigma 2^{-n}z^{n^2}} $

I've tried the root test and the ratio test but the solution they give seem inconclusive, is the any clues as to what I should do?

Thank you

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- Nov 14th 2013, 01:05 PMiPodRadius of Convergence
Hello,

I have to find the radius of convergence with this series

$\displaystyle \Sigma 2^{-n}z^{n^2}} $

I've tried the root test and the ratio test but the solution they give seem inconclusive, is the any clues as to what I should do?

Thank you - Nov 14th 2013, 01:46 PMPlatoRe: Radius of Convergence
- Nov 14th 2013, 01:56 PMiPodRe: Radius of Convergence
Oh I see, so basically it converges to 0 if |z|<1, meaning the series converges anywhere (provided |z|<1)

- Nov 14th 2013, 02:00 PMiPodRe: Radius of Convergence
Actually, |z|<2 because it's |z/2| < 1

- Nov 14th 2013, 03:20 PMPlatoRe: Radius of Convergence
NO! you were right the first time.

Look at the webpage.

You can play around with the numerator to see how it works.