# Interval of Convergance

• Feb 1st 2010, 02:54 PM
kg7150
Interval of Convergance
Find the interval of convergance of the series
$\sum_{n=1}^{\infty}\frac{3^n(x-2)^n}{\sqrt{n+2}*2^n}$

Can anyone walk me through slowly? I'm struggling a bit.
• Feb 1st 2010, 02:56 PM
Drexel28
Quote:

Originally Posted by kg7150
Find the interval of convergance of the series
$\sum_{n=1}^{\infty}\frac{3^n(x-2)^n}{\sqrt{n+2}*2^n}$

Can anyone walk me through slowly? I'm struggling a bit.

The $\frac{1}{\sqrt{n+2}}$ is irrelevant. So, you are left with $\left(\fac{3(x-2)}{2}\right)^n$. This, is of course convergent iff $\left|\frac{3(x-2)}{2}\right|<1$.
• Feb 1st 2010, 03:04 PM
kg7150
Thanks!

I've gotten that far myself. Can you tell me about the convergence at the endpoints?

Also *convergence
$\frac{1}{\sqrt{n+2}}>\frac{1}{n}$