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weird inequality

Source: Netherlands 1992

June 28, 2009
inequalitiesinequalities proposed

Problem Statement

For every positive integer n n, we define n? n? as 1?\equal{}1 and n?\equal{}\frac{n}{(n\minus{}1)?} for n≥2 n \ge 2. Prove that 1992<1992?<431992. \sqrt{1992}<1992?<\frac{4}{3} \sqrt{1992}.
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