Interval of Convergance

**kg7150** · February 1st 2010, 02:54 PM

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.

**Drexel28** · February 1st 2010, 02:56 PM

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

**kg7150** · February 1st 2010, 03:04 PM

Thanks!

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

Also *convergence
Sorry about the spelling.

**Drexel28** · February 1st 2010, 03:08 PM

Originally Posted by kg7150

Thanks!

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

Also *convergence
Sorry about the spelling.

$\frac{1}{\sqrt{n+2}}>\frac{1}{n}$

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