Power Sums With a Floor

★ 6/10Convexity algebra AM-GM inequality

Problem

Positive reals $x, y, z$ satisfy $x + y + z = 1$ . Prove that for every positive integer $n$ ,

x^n + y^n + z^n \ge \frac{1}{3^{n-1}}.

Answer

Solution

Difficulty	6/10
Topics	Convexity, algebra, AM-GM, inequality

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