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Maybe the Easiest Inequality You've Seen!

Source: 1984 National High School Mathematics League, Exam Two, Problem 5

February 22, 2020
inequalities

Problem Statement

x1,x2,⋯ ,xnx_1,x_2,\cdots,x_n are positive real numbers. Prove that x12x2+x22x3+⋯+xn2x1≥x1+x2+⋯xn.\frac{x_1^2}{x_2}+\frac{x_2^2}{x_3}+\cdots+\frac{x_n^2}{x_1}\geq x_1+x_2+\cdots x_n.
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