# Divergent series

Divergent series
Divergent Di*ver"gent, a. [Cf. F. divergent. See {Diverge}.] 1. Receding farther and farther from each other, as lines radiating from one point; deviating gradually from a given direction; -- opposed to {convergent}. [1913 Webster]

2. (Optics) Causing divergence of rays; as, a divergent lens. [1913 Webster]

3. Fig.: Disagreeing from something given; differing; as, a divergent statement. [1913 Webster]

{Divergent series}. (Math.) See {Diverging series}, under {Diverging}. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

### Look at other dictionaries:

• Divergent series — In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit. If a series converges, the individual terms of the series must approach… …   Wikipedia

• divergent series — diverguojančioji eilutė statusas T sritis fizika atitikmenys: angl. divergent series vok. divergente Reihe, f rus. расходящийся ряд, m pranc. série divergente, f …   Fizikos terminų žodynas

• divergent series — noun An infinite series whose partial sums are divergent …   Wiktionary

• Divergent — Di*ver gent, a. [Cf. F. divergent. See {Diverge}.] 1. Receding farther and farther from each other, as lines radiating from one point; deviating gradually from a given direction; opposed to {convergent}. [1913 Webster] 2. (Optics) Causing… …   The Collaborative International Dictionary of English

• 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

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• 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