# Math Help - what is the radius of convergence of that power series

1. ## what is the radius of convergence of that power series

how to determine the radius of convergence of the power series

Σ 2^(n) z^(n²).

2. ## Re: what is the radius of convergence of that power series

Originally Posted by sorv1986
how to determine the radius of convergence of the power series

Σ 2^(n) z^(n²).

I think if you try the root test you'll quickly see that the answer is $1$.

3. ## Re: what is the radius of convergence of that power series

Originally Posted by sorv1986
how to determine the radius of convergence of the power series

$\sum 2^n z^{n²}.$
Treat it as an ordinary series (rather than a power series) and use the ratio test:

$\frac{(n+1)\text{th term}}{n\text{th term}} = \frac{2^{n+1}z^{(n+1)^2}}{2^nz^{n^2}} = 2z^{2n+1}.$

The limit of that as $n\to\infty$ will depend on whether or not $|z|<1.$