翻訳と辞書 Words near each other ・ Harmonic Inc. ・ Harmonic major scale ・ Harmonic map ・ Harmonic mean ・ Harmonic measure ・ Harmonic mixer ・ Harmonic mixing ・ Harmonic morphism ・ Harmonic motion ・ Harmonic number ・ Harmonic number (disambiguation) ・ Harmonic oscillator ・ Harmonic pitch class profiles ・ Harmonic polynomial ・ Harmonic progression ・ Harmonic progression (mathematics) ・ Harmonic rhythm ・ Harmonic Scale ・ Harmonic scale ・ Harmonic scalpel ・ Harmonic series ・ Harmonic series (mathematics) ・ Harmonic series (music) ・ Harmonic seventh ・ Harmonic seventh chord ・ Harmonic spectrum ・ Harmonic superspace ・ Harmonic table note layout ・ Harmonic tremor ・ Harmonic Tremors 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 Harmonic progression (mathematics) ： ウィキペディア英語版 Harmonic progression (mathematics) In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. In other words, it is a sequence of the form :$1/a\; ,\backslash \; \backslash frac\backslash \; ,\; \backslash frac\backslash \; ,\; \backslash frac\backslash \; ,\; \backslash cdots,\; \backslash frac,$ where −a/''d'' is not a natural number and ''k'' is a natural number. (Terms in the form $\backslash frac\backslash$ can be expressed as $\backslash frac\}\}$ , we can let $\backslash frac=a$ and $\backslash frac=kd$.) Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. It is not possible for a harmonic progression (other than the trivial case where ''a'' = 1 and ''k'' = 0) to sum to an integer. The reason is that, necessarily, at least one denominator of the progression will be divisible by a prime number that does not divide any other denominator.〔. As cited by .〕 ==Examples== :12, 6, 4, 3, $\backslash tfrac$, 2, … , $\backslash tfrac$ :10, 30, −30, −10, −6, − $\backslash tfrac$, … , $\backslash tfrac\}$ 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「Harmonic progression (mathematics)」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.