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- Maclaurin's_inequality abstract "In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a1, a2, ..., an be positive real numbers, and for k = 1, 2, ..., n define the averages Sk as follows:The numerator of this fraction is the elementary symmetric polynomial of degree k in the n variables a1, a2, ..., an, that is, the sum of all products of k of the numbers a1, a2, ..., an with the indices in increasing order. The denominator is the number of terms in the numerator, the binomial coefficient Maclaurin's inequality is the following chain of inequalities:with equality if and only if all the ai are equal.For 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.".
- Maclaurin's_inequality wikiPageID "9569479".
- Maclaurin's_inequality wikiPageRevisionID "541484508".
- Maclaurin's_inequality hasPhotoCollection Maclaurin's_inequality.
- Maclaurin's_inequality id "3835".
- Maclaurin's_inequality title "MacLaurin's Inequality".
- Maclaurin's_inequality subject Category:Inequalities.
- Maclaurin's_inequality subject Category:Real_analysis.
- Maclaurin's_inequality subject Category:Symmetric_functions.
- Maclaurin's_inequality type Abstraction100002137.
- Maclaurin's_inequality type Attribute100024264.
- Maclaurin's_inequality type Difference104748836.
- Maclaurin's_inequality type Function113783816.
- Maclaurin's_inequality type Inequalities.
- Maclaurin's_inequality type Inequality104752221.
- Maclaurin's_inequality type MathematicalRelation113783581.
- Maclaurin's_inequality type Quality104723816.
- Maclaurin's_inequality type Relation100031921.
- Maclaurin's_inequality type SymmetricFunctions.
- Maclaurin's_inequality comment "In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a1, a2, ..., an be positive real numbers, and for k = 1, 2, ..., n define the averages Sk as follows:The numerator of this fraction is the elementary symmetric polynomial of degree k in the n variables a1, a2, ..., an, that is, the sum of all products of k of the numbers a1, a2, ..., an with the indices in increasing order.".
- Maclaurin's_inequality label "Disuguaglianza di MacLaurin".
- Maclaurin's_inequality label "Maclaurin's inequality".
- Maclaurin's_inequality label "麦克劳林不等式".
- Maclaurin's_inequality sameAs Disuguaglianza_di_MacLaurin.
- Maclaurin's_inequality sameAs 매클로린의_부등식.
- Maclaurin's_inequality sameAs m.02pkc44.
- Maclaurin's_inequality sameAs Q647547.
- Maclaurin's_inequality sameAs Q647547.
- Maclaurin's_inequality sameAs Maclaurin's_inequality.
- Maclaurin's_inequality wasDerivedFrom Maclaurin's_inequality?oldid=541484508.
- Maclaurin's_inequality isPrimaryTopicOf Maclaurin's_inequality.