A mathematical series is the sum of the terms of a sequence of numbers. It can be finite, meaning it has a specific number of terms, or infinite, where the terms continue indefinitely. Series are often expressed using summation notation, which provides a concise way to represent the addition of many terms. One common type of series is the arithmetic series, where each term increases by a constant value. Another important type is the geometric series, where each term is multiplied by a constant factor. Understanding these series is essential in various fields, including calculus and finance.