Definition:Series/General

Definition
Let $\left({S, \circ}\right)$ be a semigroup.

Let $\left \langle {a_n} \right \rangle$ be a sequence in $S$.

A series is what results when an infinite product is taken of $\left \langle {a_n} \right \rangle$:
 * $\displaystyle s := \sum_{n \mathop = 1}^\infty a_n = a_1 \circ a_2 \circ a_3 \circ \cdots$