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Inequality with condition an inequality

Source: Finnish Mathematics Competition 2001, Final Round, Problem 3

November 14, 2011
inequalitiesnumber theory unsolvednumber theory

Problem Statement

Numbers a,ba, b and cc are positive integers and 1a+1b+1c<1.\frac{1}{a}+\frac{1}{b}+\frac{ 1}{c}< 1. Show that 1a+1b+1c≤4142.\frac{1}{a}+\frac{1}{b}+\frac{ 1}{c}\leq \frac{41}{42}.
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