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The sum ∑n=0∞cos(nθ)2n\sum_{n=0}^{\infty} \frac{\cos{(n \theta)}}{2^{n}}n=0∑∞2ncos(nθ) where cosθ=15\cos{\theta} = \frac{1}{5}cosθ=51, can be expressed in the form αβ\frac{\alpha}{\beta}βα where α\alphaα and β\betaβ are coprime positive integers. Find α+β\alpha + \betaα+β.
Credit to MAΘ\ThetaΘ 1991
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