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Absolute Value Inequality for all k

Source: Canada 2019 Problem 4

March 29, 2019
absolute valueinequalitiesn-variable inequality

Problem Statement

Prove that for n>1n>1 and real numbers a0,a1,…,an,ka_0,a_1,\dots, a_n,k with a1=an−1=0a_1=a_{n-1}=0, ∣a0∣−∣an∣≤∑i=0n−2∣ai−kai+1−ai+2∣.|a_0|-|a_n|\leq \sum_{i=0}^{n-2}|a_i-ka_{i+1}-a_{i+2}|.
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