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Easiest Inequality ever

Source: Sri Lankan Mathematics Challenge Competition 2022

September 2, 2022
inequalitiesalgebraTststSri Lanka

Problem Statement

Problem 3 : Let x1,x2,⋯ ,x2022x_1,x_2,\cdots,x_{2022} be non-negative real numbers such that xk+xk+1+xk+2≤2x_k + x_{k+1}+x_{k+2} \leq 2 for all k=1,2,⋯ ,2020k = 1,2,\cdots,2020. Prove that ∑k=12020xkxk+2≤1010\sum_{k=1}^{2020}x_kx_{k+2}\leq 1010
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