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arithmetic progression

Source: Vietnam NMO 1987 Problem 1

February 4, 2009
trigonometryarithmetic sequencealgebra unsolvedalgebra

Problem Statement

Let u1 u_1, u2 u_2, … \ldots, u1987 u_{1987} be an arithmetic progression with u_1 \equal{} \frac {\pi}{1987} and the common difference π3974 \frac {\pi}{3974}. Evaluate S \equal{} \sum_{\epsilon_i\in\left\{ \minus{} 1, 1\right\}}\cos\left(\epsilon_1 u_1 \plus{} \epsilon_2 u_2 \plus{} \cdots \plus{} \epsilon_{1987} u_{1987}\right)
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