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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