MathDB
Plus minus inequality by enescu

Source: Balkan MO 1998, Problem 2

April 24, 2006
inequalitiesinductiontriangle inequalityinequalities proposed

Problem Statement

Let n≥2n\geq 2 be an integer, and let 0<a1<a2<⋯<a2n+10 < a_1 < a_2 < \cdots < a_{2n+1} be real numbers. Prove the inequality a1n−a2n+a3n−⋯+a2n+1n<a1−a2+a3−⋯+a2n+1n. \sqrt[n]{a_1} - \sqrt[n]{a_2} + \sqrt[n]{a_3} - \cdots + \sqrt[n]{a_{2n+1}} < \sqrt[n]{a_1 - a_2 + a_3 - \cdots + a_{2n+1}}. Bogdan Enescu, Romania
Back to ProblemsView on AoPS