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LHS < 1 implies LHS’ >1

Source: Romanian District Olympiad 2016, Grade IX, Problem 3

October 4, 2018
inequalities

Problem Statement

Let be nonnegative real numbers a,b,c, a,b,c, holding the inequality: ∑cycab+c+1≤1. \sum_{\text{cyc}} \frac{a}{b+c+1} \le 1. Prove that ∑cyc1b+c+1≥1. \sum_{\text{cyc}} \frac{1}{b+c+1} \ge 1.
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