madhavamathcompetition.com
Inequalities and mathematical induction: RMO sample problems-solutions
Problem: 1. Prove the inequality —- $latex 2^{n}(n!)^{2} \leq (2n)!$ for all natural numbers greater than or equal to 1. Proof 1: First consider the following: $latex 2.6. 10.14 \ldots (4n-2)…