Power Series Convergence Radius

**tbyou87** · December 10th 2007, 08:02 PM

Find the radius of convergence of R of the following power series.

$\sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k}$

I don't know what to do with the $x^{2k}$ term.

Thanks

**Jhevon** · December 10th 2007, 08:18 PM

Originally Posted by tbyou87

Find the radius of convergence of R of the following power series.

$\sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k}$

I don't know what to do with the $x^{2k}$ term.

Thanks

did you try the root test?

**ThePerfectHacker** · December 10th 2007, 08:20 PM

Originally Posted by tbyou87

Find the radius of convergence of R of the following power series.

$\sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k}$

I don't know what to do with the $x^{2k}$ term.

Thanks

Use the root test,
$\left| \frac{k2^k}{3^k}x^{2k} \right|^{1/k} = \frac{2}{3}k^{1/k}x^2$ the limit of $k^{1/k}\to 1$ thus:
$|a_kx^{2k}|^{1/k} \to \frac{2}{3}x^2$ .
We require that,
$\frac{2}{3}x^2 < 1 \implies x^2 < \frac{3}{2}$ .

Thread: Power Series Convergence Radius

LinkBack

Thread Tools

Display

Power Series Convergence Radius

Similar Math Help Forum Discussions

what is the radius of convergence of that power series

radius of convergence of the power series

the radius of convergence of the power series

Radius of Convergence of Power Series

power series, radius of convergence.

Search Tags