Definitions for convergent series
con·ver·gent se·ries

WiktionaryRate this definition:3.0 / 1 vote

1. convergent seriesnoun

   An infinite series whose partial sums converge

WikipediaRate this definition:0.0 / 0 votes

1. Convergent series

   In mathematics, a series is the sum of the terms of an infinite sequence of numbers. Given an infinite sequence ( a 1 , a 2 , a 3 , … ) , {\displaystyle (a_{1},a_{2},a_{3},\dots ),} the nth partial sum Sn is the sum of the first n terms of the sequence. That is, S n = ∑ k = 1 n a k . {\displaystyle S_{n}=\sum _{k=1}^{n}a_{k}.} A series is convergent if the sequence of its partial sums ( S 1 , S 2 , S 3 , … ) {\displaystyle (S_{1},S_{2},S_{3},\dots )} tends to a limit; that means that the partial sums become closer and closer to a given 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 arbitrarily small positive number ε {\displaystyle \varepsilon } , there is a (sufficiently large) integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , | S n − ℓ | ≤ ε . {\displaystyle \left|S_{n}-\ell \right\vert \leq \varepsilon .} If the series is convergent, the number ℓ {\displaystyle \ell } (necessarily unique) is called the sum of the series. Any series that is not convergent is said to be divergent.

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1. Convergent series

   In mathematics, a series is the sum of the terms of a sequence of numbers. Given a sequence, the nth partial sum is the sum of the first n terms of the sequence, that is, A series is convergent if the sequence of its partial sums converges. In more formal language, a series converges if there exists a limit such that for any arbitrarily small positive number, there is a large integer such that for all, A series that is not convergent is said to be divergent.

How to pronounce convergent series?

1. Alex

   US English

   David

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Australian

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How to say convergent series in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of convergent series in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of convergent series in Pythagorean Numerology is: 9

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Convergent_Series
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Convergent_Series
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=convergent series