Math Help - Radius of Convergence

Hello,
I have to find the radius of convergence with this series

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

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

Originally Posted by iPod
Hello,
I have to find the radius of convergence with this series

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

I've tried the root test
The root test works. For what values does ${\lim _{n \to \infty }}\frac{{{z^n}}}{2}$ converge?

Oh I see, so basically it converges to 0 if |z|<1, meaning the series converges anywhere (provided |z|<1)

Actually, |z|<2 because it's |z/2| < 1