Common
QM–AM–GM–HM inequalities
Chain of inequalities of means of positive numbers
QM–AM–GM–HM inequalities
In mathematics, the QM–AM–GM–HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean (HM), geometric mean (GM), arithmetic mean (AM), and quadratic mean (QM; also known as root mean square). Suppose that x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} are positive real numbers. Then n 1 x 1 + 1 x...
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