翻訳と辞書 Words near each other ・ Direct numerical simulation ・ Direct operations ・ Direct part marking ・ Direct participation program ・ Direct borohydride fuel cell ・ Direct bs/md ・ Direct cable connection ・ Direct carbon fuel cell ・ Direct care ・ Direct case ・ Direct changeover ・ Direct Cinema ・ Direct Client-to-Client ・ Direct Clustering Algorithm ・ Direct commission officer ・ Direct comparison test ・ Direct connect ・ Direct Connect (protocol) ・ Direct Consular Filing ・ Direct Contact ・ Direct conversion ・ Direct cool ・ Direct corporate access ・ Direct coupled ・ Direct coupling ・ Direct current ・ Direct debit ・ Direct debit dividend contributions ・ Direct democracy ・ Direct Democracy (Poland) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Direct comparison test ： ウィキペディア英語版 Direct comparison test In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing the convergence or divergence of an infinite series or an improper integral. In both cases, the test works by comparing the given series or integral to one whose convergence properties are known. == For series == In calculus, the comparison test for series typically consists of a pair of statements about infinite series with nonnegative (real-valued) terms:〔Ayres & Mendelson (1999), p. 401.〕 * If the infinite series $\backslash sum\; b\_n$ converges and $0\; \backslash le\; a\_n\; \backslash le\; b\_n$ for all sufficiently large ''n'' (that is, for all $n>N$ for some fixed value ''N''), then the infinite series $\backslash sum\; a\_n$ also converges. * If the infinite series $\backslash sum\; b\_n$ diverges and $0\; \backslash le\; b\_n\; \backslash le\; a\_n$ for all sufficiently large ''n'', then the infinite series $\backslash sum\; a\_n$ also diverges. Note that the series having larger terms is sometimes said to ''dominate'' (or ''eventually dominate'') the series with smaller terms.〔Munem & Foulis (1984), p. 662.〕 Alternatively, the test may be stated in terms of absolute convergence, in which case it also applies to series with complex terms:〔Silverman (1975), p. 119.〕 * If the infinite series $\backslash sum\; b\_n$ is absolutely convergent and $|a\_n|\; \backslash le\; |b\_n|$ for all sufficiently large ''n'', then the infinite series $\backslash sum\; a\_n$ is also absolutely convergent. * If the infinite series $\backslash sum\; b\_n$ is not absolutely convergent and $|b\_n|\; \backslash le\; |a\_n|$ for all sufficiently large ''n'', then the infinite series $\backslash sum\; a\_n$ is also not absolutely convergent. Note that in this last statement, the series $\backslash sum\; a\_n$ could still be conditionally convergent; for real-valued series, this could happen if the ''an'' are not all nonnegative. The second pair of statements are equivalent to the first in the case of real-valued series because $\backslash sum\; c\_n$ converges absolutely if and only if $\backslash sum\; |c\_n|$, a series with nonnegative terms, converges. 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「Direct comparison test」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.