what is series in math

In mathematics, a series is the operation of adding infinitely many quantities, one after the other, to a given starting quantity. A series is the sum of the terms in a sequence, which is an ordered collection of elements in which repetitions of any sort are allowed. 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 (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics, and finance. A series can be highly generalized as the sum of all the terms in a sequence, but there has to be a definite relationship between all the terms of the sequence. A mathematical series is the sum of a list of numbers that are generated according to some pattern or rule.