A series is the sum of the terms of a sequence, which is an ordered list of numbers. For example, in the series a_1, a_2, a_3, ..., each term represents a specific value in the sequence. The series can be finite, with a limited number of terms, or infinite, continuing indefinitely. Mathematically, a series can be expressed as S = a_1 + a_2 + a_3 + ... + a_n for a finite series, or S = a_1 + a_2 + a_3 + ... for an infinite series. Series are important in various fields, including mathematics, physics, and finance, for analyzing patterns and making calculations.