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Mathematics of Computation

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On lower and upper bounds of the difference between the arithmetic and the geometric mean


Author: S. H. Tung
Journal: Math. Comp. 29 (1975), 834-836
MSC: Primary 26A87
DOI: https://doi.org/10.1090/S0025-5718-1975-0393393-9
MathSciNet review: 0393393
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Abstract: Lower and upper bounds of the difference between the arithmetic and the geometric mean of n quantities are given here in terms of n, the smallest value a and the largest value A of given n quantities. Also, an upper bound for the difference, independent of n, is given in terms of a and A. All the bounds obtained are sharp.


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DOI: https://doi.org/10.1090/S0025-5718-1975-0393393-9
Keywords: Arithmetic and geometric mean, inequality, lower and upper bounds
Article copyright: © Copyright 1975 American Mathematical Society