SE-SKOLORNAS 1999 Problem 5

$x_i$ are non-negative reals. $x_1 + x_2 + ...+ x_n = s$ . Show that $x_1x_2 + x_2x_3 + ... + x_{n-1}x_n \le \frac{s^2}{4}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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