alternating series

alternating series
a series, usually infinite, in which successive terms have opposite signs, as 1 - ½ + ¼ - 1/8 + . ...

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  • Alternating series — In mathematics, an alternating series is an infinite series of the form:sum {n=0}^infty ( 1)^n,a n,with an ≥ 0 (or an ≤ 0) for all n . A finite sum of this kind is an alternating sum. An alternating series converges if the terms an converge to 0… …   Wikipedia

  • alternating series — ženklamainė eilutė statusas T sritis fizika atitikmenys: angl. alternating series vok. alternierende Reihe, f; Wechselreihe, f rus. знакопеременный ряд, m; знакочередующий ряд, m pranc. série alternée, f …   Fizikos terminų žodynas

  • Alternating series test — The alternating series test is a method used to prove that infinite series of terms converge. It was discovered by Gottfried Leibniz and is sometimes known as Leibniz s test or Leibniz criterion.A series of the form:sum {n=1}^infty a n(… …   Wikipedia

  • alternating series — I. noun : a series in mathematics whose terms are alternately positive and negative II. noun : a mathematical series in which consecutive terms are alternatively positive and negative * * * Math. a series, usually infinite, in which successive… …   Useful english dictionary

  • alternating series — noun Date: circa 1909 a mathematical series in which consecutive terms are alternatively positive and negative …   New Collegiate Dictionary

  • Alternating — may refer to:In mathematics: *alternating form *alternating group *alternating series *alternating knot *alternating mapIn electronics:*alternating current …   Wikipedia

  • Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

  • Series acceleration — In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve… …   Wikipedia

  • Alternating sign matrix — In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices arise naturally when using Dodgson… …   Wikipedia

  • series — n. sequence (math.) 1) an alternating; convergent; divergent; geometric; harmonic; infinite series succession 2) an unbroken series cycle of programs, publications 3) a miniseries; TV series * * * [ sɪ(ə)riːz] TV series convergent divergent… …   Combinatory dictionary

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