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Theorem: Inequality Between the Geometric and the Arithmetic Mean

Let $a_1,\ldots,a_n$ be non-negative positive real numbers. Their geometric mean and their arithmetic mean obey the following inequality:

$$\sqrt[n]{a_1\cdots a_n}\le \frac{a_1+\cdots+a_n}n.$$

Table of Contents

Proofs: 1

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References

Bibliography

  1. Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition