# what is the radius of convergence of that power series

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• Dec 1st 2011, 09:23 PM
sorv1986
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^(nē).

thanks in advance .regards.(Rock)
• Dec 1st 2011, 10:15 PM
Drexel28
Re: what is the radius of convergence of that power series
Quote:

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

Σ 2^(n) z^(nē).

thanks in advance .regards.(Rock)

I think if you try the root test you'll quickly see that the answer is $1$.
• Dec 2nd 2011, 05:27 AM
Opalg
Re: what is the radius of convergence of that power series
Quote:

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

$\sum 2^n z^{nē}.$

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 $|z|<1.$