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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 Term test ： ウィキペディア英語版 Term test In mathematics, the ''n''th-term test for divergence〔Kaczor p.336〕 is a simple test for the divergence of an infinite series: *If $\backslash lim\_\; a\_n\; \backslash neq\; 0$ or if the limit does not exist, then $\backslash sum\_^\backslash infty\; a\_n$ diverges. Many authors do not name this test or give it a shorter name.〔For example, Rudin (p.60) states only the contrapositive form and does not name it. Brabenec (p.156) calls it just the ''nth'' term test. Stewart (p.709) calls it the Test for Divergence.〕 == Usage == Unlike stronger convergence tests, the term test cannot prove by itself that a series converges. In particular, the converse to the test is not true; instead all one can say is: *If $\backslash lim\_\; a\_n\; =\; 0,$ then $\backslash sum\_^\backslash infty\; a\_n$ may or may not converge. In other words, if $\backslash lim\_\; a\_n\; =\; 0,$ the test is inconclusive. The harmonic series is a classic example of a divergent series whose terms limit to zero.〔Rudin p.60〕 The more general class of ''p''-series, :$\backslash sum\_^\backslash infty\; \backslash frac,$ exemplifies the possible results of the test: *If ''p'' ≤ 0, then the term test identifies the series as divergent. *If 0 < ''p'' ≤ 1, then the term test is inconclusive, but the series is divergent by the integral test for convergence. *If 1 < ''p'', then the term test is inconclusive, but the series is convergent, again by the integral test for convergence. 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「Term 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.