how to determine the radius of convergence of the power series

Σ 2^(n) z^(nē).

thanks in advance .regards.(Rock)

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- Dec 1st 2011, 08:23 PMsorv1986what is the radius of convergence of that power series
how to determine the radius of convergence of the power series

Σ 2^(n) z^(nē).

thanks in advance .regards.(Rock) - Dec 1st 2011, 09:15 PMDrexel28Re: what is the radius of convergence of that power series
- Dec 2nd 2011, 04:27 AMOpalgRe: what is the radius of convergence of that power series
Treat it as an ordinary series (rather than a power series) and use the ratio test:

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

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