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$\large \lim_{x \to 0} \frac{ 1- \displaystyle \prod_{k=1}^{100} \cos kx}{x^2} = \, ?$

Bonus: Generalize for $n$ or $\displaystyle \lim_{x \to 0} \frac{ 1-\prod_{k=1}^{n} \cos kx}{x^2}$.

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