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Maximum of the sum x_ix_{i+1} in terms of p, the sum of x_i.

Source: Vietnam MO 1980 P6

March 17, 2011
inequalities proposedinequalities

Problem Statement

Let be given an integer n\ge 2 and a positive real number pp. Find the maximum of ∑i=1n−1xixi+1,\displaystyle\sum_{i=1}^{n-1} x_ix_{i+1}, where xix_i are non-negative real numbers with sum pp.
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