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Crazy Cosine Calculus!

Calculus Level 3

Let $I_m = \displaystyle \int_0^{2\pi} \cos(x) \cos(2x) \dots \cos(mx) dx$ . What is the sum of all integers $100 \leq m \leq 110$ such that $I_m \neq 0$ ?

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by Michael Tong

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