Definition of Converging series. Meaning of Converging series. Synonyms of Converging series

Here you will find one or more explanations in English for the word Converging series. Also in the bottom left of the page several parts of wikipedia pages related to the word Converging series and, of course, Converging series synonyms and on the right images related to the word Converging series.

Definition of Converging series

Converging series
Converging Con*ver"ging, a. Tending to one point; approaching each other; convergent; as, converging lines. --Whewell. Converging rays(Opt.), rays of light, which, proceeding from different points of an object, tend toward a single point. Converging series (Math.), a series in which if an indefinitely great number of terms be taken, their sum will become indefinitely near in value to a fixed quantity, which is called the sum of the series; -- opposed to a diverging series.

Meaning of Converging series from wikipedia

- series of f {\displaystyle f} converges uniformly, but not necessarily absolutely, to f {\displaystyle f} . A function ƒ has an absolutely converging...
- generally, given a converging series of vectors in a finite-dimensional real vector space E, the set of sums of converging rearranged series is an affine subspace...
- then the series is absolutely convergent. If r > 1, then the series diverges. If r = 1, the ratio test is inconclusive, and the series may converge. This...
- mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely. More precisely, a series ∑ n = 0...
- other function converging to a limit in a metric space. (See: Cauchy sequence; Limit of a sequence; Limit of a function.) Pointwise convergence Unconditional...
- mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions ( f n )...
- {\tfrac {1}{2}}\right).} The following two formulas involve quickly converging series, and are thus appropriate for numerical com****tion: G = 3 ∑ n = 0...
- number when the number of their terms increases. More precisely, a series converges, if there exists a number ℓ {\displaystyle \ell } such that for every...
- In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the...
- Convergence is a series of books edited by Ruth Nanda Anshen and published by the Columbia University Press dealing with ideas that changed, or that are...
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