Inequalities for Math Olympiad: Proof Techniques with Transitivity and Expanding/Shrinking

This is part of the Inequality for Math Olympiad Series. We introduced the very useful proof technique of expanding or shrinking on inequality. Two example proofs are presented.

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00:00:00 Introduction: Problem Statement
00:00:39 Transitivity, Expanding and Shrinking Techniques
00:02:17 Example 1
00:05:00 Example 2
00:05:26 Sqrt Function is Concave
00:07:20 Proof of Example 2
00:13:05 Convergence of the Summation
00:13:48 Riemann-Zeta Function
00:14:01 Summary