Difference between revisions of "Arithmetic MeanGeometric Mean Inequality"
m (uncapitalised names of means) 
m (Arithmetic MeanGeometric Mean moved to Arithmetic meangeometric mean: no need for capital letters) 
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Revision as of 14:37, 18 June 2006
The Arithmetic MeanGeometric Mean (AMGM) Inequality states that the arithmetic mean of a set of positive real numbers is greater than or equal to the geometric mean of the same set of positive real numbers. For example, for the set , the Arithmetic Mean, 25, is greater than the Geometric Mean, 18; AMGM guarantees this is always the case.
In general, AMGM states that for a set of positive real numbers , the following always holds:
The AMGM inequalitiy is a specific case of the Power mean inequality. It (and the much more general Power Mean Inequality) are used fairly frequently to solve Olympiadlevel Inequality problems, such as those on the USAMO and IMO.