Definition:Series/General

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

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

Let $\left \langle {s_N} \right \rangle$ be the sequence defined as:
 * $\displaystyle s_N = \sum_{n \mathop = 1}^N a_n = a_1 \circ a_2 \circ \cdots \circ a_N$

Then $\left \langle {s_N} \right \rangle$ is called the sequence of partial products of the series $\displaystyle \sum_{n \mathop = 1}^\infty a_n$.