1982•International Journal of Mathematical Education in Science and TechnologyRequires access

Proofs of the arithmetic mean‐geometric mean inequality

Dieter Rüthing

Abstract

The aim of this paper is to present several proofs of the arithmetic mean‐geometric mean inequality using mathematical induction and the generalized inequality of Bernoulli. Moreover, the well‐known special ideas and procedures of Jacobsthal and Rado in proving the arithmetic mean‐geometric mean inequality are integrated into certain general ideas and procedures from a heuristic standpoint.

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Key concepts: Inequality of arithmetic and geometric means, Mathematics, Mathematical proof, Geometric mean, Harmonic mean, Inequality, Arithmetic, Calculus (dental)