Series

A series is the result of adding together the terms of a sequence. For example, given the sequence below:

The series is the sum of the terms of this sequence typically written using the summation symbol:

Series can be finite or infinite. A critical concept associated with infinite series is convergence. An infinite series converges if the sum approaches a finite value as the number of terms increases indefinitely. Conversely, if the sum does not approach a finite value, the series diverges.

Sequence

A sequence is an ordered list of numbers (also called terms) that often follow a specific pattern or rule. Each term in the sequence has a unique position denoted by a positive integer, usually represented by the variable n.