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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 telescoping series ： ウィキペディア英語版 telescoping series In mathematics, a telescoping series is a series whose partial sums eventually only have a fixed number of terms after cancellation.〔Tom M. Apostol, ''Calculus, Volume 1,'' Blaisdell Publishing Company, 1962, pages 422–3〕〔Brian S. Thomson and Andrew M. Bruckner, ''Elementary Real Analysis, Second Edition'', CreateSpace, 2008, page 85〕 Such a technique is also known as the method of differences. For example, the series :$\backslash sum\_^\backslash infty\backslash frac$ (the series of reciprocals of pronic numbers) simplifies as :$\backslash begin$ \sum_^\infty \frac & - \frac \right) \\ \sum_^N \left( \frac - \frac \right) \\ \left\lbrack \right) + \left(\frac - \frac\right) + \cdots + \left(\frac - \frac\right) } \right\rbrack \\ \left\lbrack + \frac\right) + \left( - \frac + \frac\right) + \cdots + \left( - \frac + \frac\right) - \frac } \right\rbrack \\ \left\lbrack } \right\rbrack = 1. \end ==In general== Let $a\_n$ be a sequence of numbers. Then, :$\backslash sum\_^N\; \backslash left(a\_n\; -\; a\_\backslash right)\; =\; a\_N\; -\; a\_,$ and, if $a\_n\; \backslash rightarrow\; 0$ :$\backslash sum\_^\backslash infty\; \backslash left(a\_n\; -\; a\_\backslash right)\; =\; -\; a\_.$ 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「telescoping series」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.