# 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 $$pq$$.

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