Acta Mathematica Nitriensia Vol. 2, No. 2, 2016

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Marek Varga, Peter Michalička:	Arithmetic Mean and Geometric Mean
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Abstract: In mathematics we define several types of means. Probably the most known are the arithmetic and geometric means. If we are given n nonnegative numbers x1, x2, ... xn; then the number An = (x1 + x2 + ... + xn) / n we call the arithmetic mean and the number Gn = nthroot(x1 * x2 * ... * xn) we call the geometric mean of the numbers given. In the first part of the paper with the use of functions' their of more variables we will show that for each natural number n An >= Gn applies. In the second part we will try to show the same, however, without using the differential calculus.

Keywords: arithmetic mean, geometric mean, proof, differential calculus

Classification: E55

Pages: 43 – 48

DOI: 10.17846/AMN.2016.2.2.43-48

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