Find the interval of convergance of the series
$\displaystyle \sum_{n=1}^{\infty}\frac{3^n(x-2)^n}{\sqrt{n+2}*2^n}$
Can anyone walk me through slowly? I'm struggling a bit.
The $\displaystyle \frac{1}{\sqrt{n+2}}$ is irrelevant. So, you are left with $\displaystyle \left(\fac{3(x-2)}{2}\right)^n$. This, is of course convergent iff $\displaystyle \left|\frac{3(x-2)}{2}\right|<1$.