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| − | In [[algebra]], the '''AM-GM inequality''', shorthand for the '''inequality of arithmetic and geometric means''', states that the arithmetic mean is greater than or equal to the geometric mean of any list of nonnegative reals; furthermore, equality holds if and only if every real in the list is the same.
| + | #REDIRECT[[AM-GM Inequality]] |
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| − | In symbols, the inequality states that for any <math>x_1, x_2, \ldots, x_n \geq 0</math>, <cmath>\frac{x_1 + x_2 + \cdots + x_n}{n} \geq \sqrt[n]{x_1 x_2 \cdots x_n},</cmath> with equality if and only if <math>x_1 = x_2 = \cdots = x_n</math>.
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| − | '''NOTE''': This article is a work-in-progress and meant to replace the [[Arithmetic mean-geometric mean inequality]] article, which is of poor quality.
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| − | OUTLINE:
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| − | * Proofs
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| − | ** Links to [[Proofs of AM-GM Inequality]]
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| − | **
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| − | * Generalizations
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| − | ** Weighted AM-GM
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| − | ** QM-AM-GM-HM (with or without weights)
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| − | ** Power Mean (with or without weights)
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