Maclaurin's inequality [SEP] named after
Maclaurin's inequality
In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. 
Let "a", "a", ..., "a" be positive real numbers, and for "k" = 1, 2, ..., "n" define the averages "S" as follows:
The numerator of this fraction is the elementary symmetric polynomial of degree "k" in the "n
"n" = 2, this gives the usual inequality of arithmetic and geometric means of two numbers. Maclaurin's inequality is well illustrated by the case "n" = 4:
Maclaurin's inequality can be proved using the Newton's inequalities.
See also.
- Newton's inequalities
- Muirhead's inequality
- Generalized mean inequality