summation of divergent series

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• 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 geometric series — In mathematics, an infinite geometric series of the form is divergent if and only if | r | ≥ 1. Methods for summation of divergent series are sometimes useful, and usually evaluate divergent geometric series to a sum that… …   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

• 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

• Summation of Grandi's series — General considerationstability and linearityThe formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include: *Adding or subtracting two series term by term, *Multiplying through by a scalar term by term, *… …   Wikipedia

• Summation by parts — In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. The summation by parts formula is sometimes called… …   Wikipedia

• Summation — For evaluation of sums in closed form see evaluating sums. : Summation is also a term used to describe a process in synapse biology. Summation is the addition of a set of numbers; the result is their sum or total . The numbers to be summed may be …   Wikipedia

• summation method — Math. a method for associating a sum with a divergent series. * * * …   Universalium

• summation method — Math. a method for associating a sum with a divergent series …   Useful english dictionary

• Ramanujan summation — is a technique invented by the mathematician Srinivasa Ramanujan for assigning a sum to infinite divergent series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it… …   Wikipedia

• Borel summation — In mathematics, a Borel summation is a generalisation of the usual notion of summation of a series. In particular it gives a definition of a quantity that in many ways behaves formally like the sum, even if the series is in fact… …   Wikipedia