Hello,

I have to find the radius of convergence with this series

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, 02:05 PMiPodRadius of Convergence
Hello,

I have to find the radius of convergence with this series

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, 02:46 PMPlatoRe: Radius of Convergence
- Nov 14th 2013, 02:56 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, 03:00 PMiPodRe: Radius of Convergence
Actually, |z|<2 because it's |z/2| < 1

- Nov 14th 2013, 04:20 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.