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unorthodox inequality

Source: Romanian District Olympiad 2015, Grade X, Problem 1

September 25, 2018
inequalitiesinductionfactorial

Problem Statement

For any n≥2 n\ge 2 natural, show that the following inequality holds: ∑i=2n1(2i)!≥n−12n+2. \sum_{i=2}^n\frac{1}{\sqrt{(2i)!}}\ge\frac{n-1}{2n+2} .
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