UA-UMO 2005 Problem 96

For every positive integer $n$ , prove the inequality:

$\frac{3}{1!+2!+3!}+\frac{4}{2!+3!+4!}+...+\frac{n+2}{n!+(n+1)!+(n+2)!}<\frac{1}{2}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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