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# infinite series

A sum with a countably infinite number of ordered summands; the sum itself is formally defined as the limit of the partial sums, if it exists.

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• infinite series — Math. a sequence of numbers in which an infinite number of terms are added successively in a given pattern; the sequence of partial sums of a given sequence. [1790 1800] * * * In mathematics, the sum of infinitely many numbers, whose relationship …   Universalium

• infinite series — begalinė eilutė statusas T sritis automatika atitikmenys: angl. infinite series vok. unendliche Reihe, f rus. бесконечный ряд, m pranc. série infinie, f …   Automatikos terminų žodynas

• infinite series — (Mathematics) sequence of numbers containing an infinite number of terms …   English contemporary dictionary

• infinite series — noun : an endless succession of terms or of factors proceeding according to some mathematical law * * * Math. a sequence of numbers in which an infinite number of terms are added successively in a given pattern; the sequence of partial sums of a… …   Useful english dictionary

• Euler on infinite series — Divergent seriesLeonhard Euler succinctly described a potential foundation for his treatment of divergent series in a calculus textbook published in 1755 [Euler (1755), Part 1, Chapter 3, #111, pp.78 79; English translation by Bromwich (p.322).… …   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

• Infinite regress — An infinite regress in a series of propositions arises if the truth of proposition P 1 requires the support of proposition P 2, and for any proposition in the series P n , the truth of P n requires the support of the truth of P n +1. There would… …   Wikipedia

• Infinite arithmetic series — In mathematics, an infinite arithmetic series is an infinite series whose terms are in an arithmetic progression. Examples are nowrap|1 + 1 + 1 + 1 + · · · and nowrap|1 + 2 + 3 + 4 + · · ·. The general form for an infinite arithmetic series… …   Wikipedia

• series — /sear eez/, n., pl. series, adj. n. 1. a group or a number of related or similar things, events, etc., arranged or occurring in temporal, spatial, or other order or succession; sequence. 2. a number of games, contests, or sporting events, with… …   Universalium

• Infinite product — In mathematics, for a sequence of numbers a 1, a 2, a 3, ... the infinite product :prod {n=1}^{infty} a n = a 1 ; a 2 ; a 3 cdotsis defined to be the limit of the partial products a 1 a 2... a n as n increases without bound. The product is said… …   Wikipedia