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- Dictionaryseries/ˈsɪəriːz/
noun
- 1. a number of events, objects, or people of a similar or related kind coming one after another: "the explosion was the latest in a series of accidents" Similar
- 2. a set or sequence of related television or radio programmes: "a new drama series" Similar
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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.
- Series Number
- Finite Series
- Infinite Series
- Properties of Series
A series may contain a number of terms in the form of numerical, functions, quantities, etc. When the series is given, it indicates the symbolised sum, not the sum itself. For example, 2 + 4 + 6 + 8 + 10 + 12 is a series with six terms. To find the sum of these numbers, we use the phrase “sum of a series”, which means the number that results from a...
A series with a countable number of terms is called a finite series. If a1 + a2 + a3 + … + anis a series with n terms and is a finite series containing n terms. Thus, Snis the sum of the series and is denoted as: Sn = ∑ an Also, we can define the sum of a specific number of terms. These are expressed as: S1 = a1 S2 = a1 + a2 S3 = a1 + a2 + a3 S4 = ...
A series with an infinite number of terms is called an infinite series. This is expressed as: Here, “i” is called the index of summation. We can use different letters to denote the index of summation. For example, All these representations are the same. We cannot effectively carry the infinite string of additionsmentioned by a series. Also, we can ...
Some of the properties of series are listed below: If ∑an and ∑bnare both convergent series, then 1. ∑ canis also convergent 2. ∑ Can = c ∑ansuch that c is any real number 3. \(\begin{array}{l}\sum_{n=k}^{\infty } a_{n}\pm \sum_{n=k}^{\infty } b_{n}\end{array} \)is also convergent 4. \(\begin{array}{l}\sum_{n=k}^{\infty } a_{n}\pm \sum_{n=k}^{\inft...
Oct 6, 2021 · 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.
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SERIES definition: 1. a number of similar or related events or things, one following another: 2. a number of games…. Learn more.
The sequence is the group or sequential arrangement of numbers in a particular order or set of rules. Series is formed by adding the digits of a sequence. Learn more about sequence and series and differences between them.
The meaning of SERIES is a number of things or events of the same class coming one after another in spatial or temporal succession. How to use series in a sentence.
A "series" is what you get when you add up all the terms of a sequence; the addition, and also the resulting value, are called the "sum" or the "summation". For instance, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the sum "1 + 2 + 3 + 4", and the value of the series is 10.
