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Putnam 1978 A5

Source: Putnam 1978

May 3, 2022
PutnamtrigonometryinequalitiesJensen s Inequality

Problem Statement

Let 0<xi<π0 < x_i < \pi for i=1,2,…,ni=1,2,\ldots, n and set x=x1+x2+…+xnn.x= \frac{ x_1 +x_2 + \ldots+ x_n }{n}. Prove that ∏i=1nsin⁡xixi≤(sin⁡xx)n. \prod_{i=1}^{n} \frac{ \sin x_i }{x_i } \leq \left( \frac{ \sin x}{x}\right)^{n}.
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