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Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Like a set, it contains members (also called elements, or terms).
The number of elements (possibly infinite) is called the length of the sequence.

Unlike a set, the same elements can appear multiple times at different positions in a sequence,
and unlike a set, the order does matter.

Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers
(for infinite sequences), or the set of the first n natural numbers (for a sequence of finite length n).

Series is a description of the operation of adding infinitely many quantities,
one after the other, to a given starting quantity.[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
(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.