A Power Inequality from a Harmonic Condition

★ 6/10algebra Binomial Theorem AM-GM inequality

Problem

Let $a$ and $b$ be positive numbers with $\dfrac{1}{a} + \dfrac{1}{b} = 1$ , and let $n \in \mathbb{N}^*$ . Prove that

(a+b)^n - a^n - b^n \geqslant 2^{2n} - 2^{n+1}.

Answer

Solution

Difficulty	6/10
Topics	algebra, Binomial Theorem, AM-GM, inequality

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