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Maximizing a sum !

Source: Romania TST Day 5 Problem 3

January 21, 2015
inequalities unsolvedinequalitiesalgebra

Problem Statement

Let nn a positive integer and let f ⁣:[0,1]→Rf\colon [0,1] \to \mathbb{R} an increasing function. Find the value of : max⁡0≤x1≤⋯≤xn≤1∑k=1nf(∣xk−2k−12n∣) \max_{0\leq x_1\leq\cdots\leq x_n\leq 1}\sum_{k=1}^{n}f\left ( \left | x_k-\frac{2k-1}{2n} \right | \right )
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