VMO 1980 Problem 6

Given n > 1 and real s > 0, find the maximum of $x_1x_2$ + $x_2x_3$ + $x_3x_4$ + ... + $x_{n-1}x_n$ for non-negative reals $x_i$ such that $x_1$ + $x_2$ + ... + $x_n$ = s.

Community text Kalva (prase.cz mirror). Quoted with source.

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