# Being endlessly productive

**Geometry**Level 3

When \[\prod_{k=2}^{\infty}\cos\left(\frac{\pi}{2^k}\right)\]

is computed, the result is \(a\pi^b\) for integers \(a\) and \(b.\) What is \(a+b?\)

When \[\prod_{k=2}^{\infty}\cos\left(\frac{\pi}{2^k}\right)\]

is computed, the result is \(a\pi^b\) for integers \(a\) and \(b.\) What is \(a+b?\)

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