A calculus problem by Ryan Broder

Calculus Level 4

\[f(x) = \lim_{n \to +\infty} \ \prod_{k=1}^{n} \cos{\frac{x}{2^k}}\] \[\lim_{a \to +\infty} \sum_{x=-a}^{a} f(x)=N\] What is \(\lfloor {100N} \rfloor\)?

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