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.

**[1]**E. F. BECKENBACH & R. E. BELLMAN,*Inequalities*, 2nd rev. ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 30, Springer-Verlag, New York, 1965. MR**33**#236. MR**0192009 (33:236)****[2]**C. LOEWNER & H. B. MANN, "On the difference between the geometric and the arithmetic mean of*n*quantities,"*Advances in Math.*, v. 5, 1971, pp. 472-473. MR**43**#4982. MR**0279259 (43:4982)**

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Additional Information

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