MathDB
x_1^2x_2^2...x_n^2+x_2^2x_3^2...x_{n+1}^2+...+x_{2n}^2x_1^2...x_{n-1}^2<1/n^{2n}

Source: Romania IMO TST 1991 p8

February 19, 2020
inequalitiesSumalgebra

Problem Statement

Let x1,x2,...,x2nx_1,x_2,...,x_{2n} be positive real numbers with the sum 11. Prove that x12x22...xn2+x22x32...xn+12+...+x2n2x12...xn−12<1n2nx_1^2x_2^2...x_n^2+x_2^2x_3^2...x_{n+1}^2+...+x_{2n}^2x_1^2...x_{n-1}^2 <\frac{1}{n^{2n}}
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