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Found problems: 1

2017 Korea USCM, 7
Tags: trigonometry , real analysis , series , trigonometric series , inequalities
Prove the following inequality holds if $\{a_n\}$ is a deceasing sequence of positive reals, and $0<\theta<\frac{\pi}{2}$. $$\left|\sum_{n=1}^{2017} a_n \cos n\theta \right| \leq \frac{\pi a_1}{\theta}$$