MacLaurin’s inequality

Let a1,a2,,an be positive real numbers , and define the sums Sk as follows :


Then the following chain of inequalitiesMathworldPlanetmath is true :


Note : Sk are called the averagesMathworldPlanetmath of the elementary symmetricPlanetmathPlanetmath sums
This inequality is in fact important because it shows that the arithmetic-geometric mean inequality is nothing but a consequence of a chain of stronger inequalities

Title MacLaurin’s inequality
Canonical name MacLaurinsInequality
Date of creation 2013-03-22 13:19:28
Last modified on 2013-03-22 13:19:28
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 7
Author Mathprof (13753)
Entry type Definition
Classification msc 26D15