# 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

2. ## Re: Radius of Convergence

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?

3. ## Re: Radius of Convergence

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

4. ## Re: Radius of Convergence

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

5. ## Re: Radius of Convergence

Originally Posted by iPod
Actually, |z|<2 because it's |z/2| < 1
NO! you were right the first time.

Look at the webpage.

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