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For b>1b>1b>1 and cosx=a\cos x = acosx=a, find the value of :
∑r=0∞cos(rx)br\displaystyle \sum_{r=0}^{\infty} \frac{\cos(rx)}{b^r}r=0∑∞brcos(rx).
If for b=32b = \frac{3}{2}b=23 and a=12 a = \frac{1}{2}a=21, this value can be expressed as pq\frac{p}{q}qp,where ppp and qqq are coprimes, then find pqpqpq.
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