Infinite sum

Calculus Level 5

For $b>1$ and $\cos x = a$ , find the value of :

$\displaystyle \sum_{r=0}^{\infty} \frac{\cos(rx)}{b^r}$ .

If for $b = \frac{3}{2}$ and $a = \frac{1}{2}$ , this value can be expressed as $\frac{p}{q}$ ,where $p$ and $q$ are coprimes, then find $pq$ .