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In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions.
In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount. We use series in many areas of mathematics, even for studying finite structures, for example, combinatorics for forming functions.
A series is the sum of the terms in a sequence. The sum of the first \(n\) terms is called the \(n\)th partial sum and is denoted \(S_{n}\). Use sigma notation to denote summations in a compact manner.
What is a Sequence? A Sequence is a list of things (usually numbers) that are in order. Infinite or Finite. When the sequence goes on forever it is called an infinite sequence, otherwise it is a finite sequence. Examples: {1, 2, 3, 4, ...} is a very simple sequence (and it is an infinite sequence) {20, 25, 30, 35, ...} is also an infinite sequence.
A mathematical series is an infinite sum of the elements in some sequence. A series with terms \(a_n\), where \(n\) varies from \(1\) through all positive integers, is expressed as \[ \sum_{n= 1}^\infty a_n.
Series. In mathematics, the term series is typically used to describe an infinite series. An infinite series is the sum of an infinite sequence. Series can either converge or diverge. When a series converges, it is a single value, since it is the sum of an infinite sequence.
Explains the basic terminology and notation of sequences and series, including summation symbols, subscripts, and indices.
