A Sum of Absolute Lines

★ 8/10Convexity Absolute Value algebra AM-GM inequality

Problem

Let $n$ be a positive integer and $x \in \mathbb{R}$ . Prove that

\sum_{i=1}^n |ix - 1| \geqslant \sqrt{2n^2 + 2n} - n - 1.

Answer

Solution

Difficulty	8/10
Topics	Convexity, Absolute Value, algebra, AM-GM, inequality

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