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max of x_1x_2 + x_2x_3 + ... + x_{n-1}x_n if sum x_1=1, x_1>0

Source: VI - Rioplatense 1997 L3 P5

September 19, 2022
algebrainequalities

Problem Statement

Let x1,x2,...,xnx_1, x_2, ... , x_n be non-negative numbers n≥3n\ge3 such that x1+x2+...+xn=1x_1 + x_2 + ... + x_n = 1. Determine the maximum possible value of the expression x1x2+x2x3+...+xn−1xnx_1x_2 + x_2x_3 + ... + x_{n-1}x_n.
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