Concepts
Series
Also Known As Infinite Series
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The result of adding the terms of a sequence together, one after another, continued without end. A series may settle toward a finite total as more terms are added, in which case it converges, or its partial sums may grow or oscillate without settling, in which case it diverges.
Facts
Disputed
Origin YearOne of two specific candidate years recorded for series, both from the same Wikipedia History of the theory of infinite series section: 1668 is the first attestation of the core convergence and divergence terminology (James Gregory); 1821 (recorded alongside this fact) is Cauchy's Cours d'Analyse, widely credited with starting the rigorous modern theory. Ancient Greek summation methods, such as Archimedes' method for areas, predate both but carry no specific year in the source. No single year is treated as definitive. Origin YearSecond of two recorded candidate years for series; see the 1668 entry for the fuller note. Cauchy's 1821 Cours d'Analyse begins the rigorous modern theory of convergence tests. Cross-Tradition Connections
Sources
1. Series, Mathematics (Wikipedia)
Wikimedia FoundationDefinition sectionQuote, Definition section
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other.
1. Series, Mathematics (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
The mathematical side of Zeno's paradoxes was resolved using the concept of a limit during the 17th century, especially through the early calculus of Isaac Newton. The resolution was made more rigorous and further improved in the 19th century through the work of Carl Friedrich Gauss and Augustin-Louis Cauchy.
1. Series, Mathematics (Wikipedia)
Wikimedia FoundationHistory of the theory of infinite series sectionQuote, History of the theory of infinite series section
Cauchy (1821) insisted on strict tests of convergence... and with him begins the discovery of effective criteria.
1. Series, Mathematics (Wikipedia)
Wikimedia Foundationlead section, contrasted with finite seriesQuote, lead section, contrasted with finite series
To emphasize that there are an infinite number of terms, series are often also called infinite series to contrast with finite series
1. Series, Mathematics (Wikipedia)
Wikimedia FoundationIn Branch: Analysis, Lead sectionQuote, In Branch: Analysis, Lead section
The study of series is a major part of calculus and its generalization, mathematical analysis.
Wolfram MathWorld
Wolfram Research, Inc.https://mathworld.wolfram.com/Series.htmlQuote, https://mathworld.wolfram.com/Series.html
A series is an infinite ordered set of terms combined together by the addition operator.
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