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Maclaurin’s Inequality and a Generalized Bernoulli Inequality

Iddo Ben-Ari and Keith Conrad
Mathematics Magazine
Vol. 87, No. 1 (February 2014), pp. 14-24
DOI: 10.4169/math.mag.87.1.14
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.1.14
Page Count: 11
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Maclaurin’s Inequality and a Generalized Bernoulli Inequality
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Abstract

Summary Maclaurin’s inequality is a natural, but nontrivial, generalization of the arithmetic-geometric mean inequality. We present a new proof that is based on an analogous generalization of Bernoulli’s inequality. Applications of Maclaurin’s inequality to iterative sequences and probability are discussed, along with graph-theoretic versions of the Maclaurin and Bernoulli inequalities.

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