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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 Irrationality sequence ： ウィキペディア英語版 Irrationality sequence In mathematics, a sequence of positive integers ''a''''n'' is called an irrationality sequence if it has the property that, for every sequence ''x''''n'' of positive integers, the sum of the series :$\backslash sum\_^\backslash infty\; \backslash frac$ exists (that is, it converges) and is an irrational number.〔.〕〔.〕 The problem of characterizing irrationality sequences was posed by Paul Erdős and Ernst G. Straus, who originally called the property of being an irrationality sequence "Property P".〔.〕 ==Examples== The powers of two whose exponents are powers of two, $2^$, form an irrationality sequence. However, although Sylvester's sequence :2, 3, 7, 43, 1807, 3263443, ... (in which each term is one more than the product of all previous terms) also grows doubly exponentially, it does not form an irrationality sequence. For, letting $x\_n=1$ gives :$\backslash frac+\backslash frac+\backslash frac+\backslash frac+\backslash cdots=1,$ a series converging to a rational number. Likewise, the factorials $n!$ do not form an irrationality sequence, because the sequence $x\_n=n+2$ leads to a series with a rational sum, :$\backslash sum\_^\backslash frac=\backslash frac+\backslash frac+\backslash frac+\backslash frac+\backslash frac+\backslash cdots=1.$〔 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「Irrationality sequence」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.