Definition:Series/General

Definition
Let $\struct{S, \circ}$ be a semigroup.

Let $\sequence{a_n}$ be a sequence in $S$.

Informally, a series is what results when an infinite product is taken of $\sequence {a_n}$:
 * $\ds s := \sum_{n \mathop = 1}^\infty a_n = a_1 \circ a_2 \circ a_3 \circ \cdots$

Formally, a series is a sequence in $S$.