\begin{definition}[Definition:Series/General/Sequence of Partial Products]
Let $\struct {S, \circ}$ be a semigroup.
Let $\sequence {a_n}$ be a sequence in $S$.
Let $s$ be the the series:
:$\ds s = \sum_{n \mathop = 1}^\infty a_n = a_1 \circ a_2 \circ a_3 \circ \cdots$
The sequence $\sequence {s_N}$ defined as the indexed iterated operation:
:$\ds s_N = \sum_{n \mathop = 1}^N a_n = a_1 \circ a_2 \circ \cdots \circ a_N$
is the '''sequence of partial products''' of the series $\ds \sum_{n \mathop = 1}^\infty a_n$.
Category:Definitions/Abstract Algebra
Category:Definitions/Series
\end{definition}