# Math Help - Interval of Convergance

1. ## 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.

2. 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 $\left|\frac{3(x-2)}{2}\right|<1$.

3. Thanks!

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

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