\begin{definition}[Definition:Series/General]
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 $S$.
\end{definition}