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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:

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

| | | | | created: 2020-02-02 13:34:05 | modified: 2020-02-02 13:35:00 | by: bookofproofs | references: [586]

1.Proof: (related to "Inequality Between the Geometric and the Arithmetic Mean")

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[586] Heuser Harro: “Lehrbuch der Analysis, Teil 1”, B.G. Teubner Stuttgart, 1994, 11. Auflage