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Maximum value of cyclic sum

Source: Romania 2017 IMO TST 2, problem 3

March 18, 2018
inequalities

Problem Statement

Given an interger n≥2n\geq 2, determine the maximum value the sum a1a2+a2a3+...+an−1an\frac{a_1}{a_2}+\frac{a_2}{a_3}+...+\frac{a_{n-1}}{a_n} may achieve, and the points at which the maximum is achieved, as a1,a2,...ana_1,a_2,...a_n run over all positive real numers subject to ak≥a1+a2...+ak−1a_k\geq a_1+a_2...+a_{k-1}, for k=2,...nk=2,...n
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