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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maclaurin's inequality ： ウィキペディア英語版 Maclaurin's inequality In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let ''a''1, ''a''2, ..., ''a''''n'' be positive real numbers, and for ''k'' = 1, 2, ..., ''n'' define the averages ''S''''k'' as follows: :$S\_k\; =\; \backslash frac\; a\_\; \backslash cdots\; a\_\}.$ Maclaurin's inequality is the following chain of inequalities: :$S\_1\; \backslash geq\; \backslash sqrt\; \backslash geq\; \backslash sqrt()\; \backslash geq\; \backslash cdots\; \backslash geq\; \backslash sqrt()$ with equality if and only if all the ''a''''i'' are equal. For ''n'' = 2, this gives the usual inequality of arithmetic and geometric means of two numbers. Maclaurin's inequality is well illustrated by the case ''n'' = 4: : $$ \begin & \\() & } \\() & } \\() & Maclaurin's inequality can be proved using the Newton's inequalities. ==See also== * Newton's inequalities * Muirhead's inequality * Generalized mean inequality 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maclaurin's inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.