\begin{definition}[Definition:Sequence of Partial Products]
Let $p$ be the infinite product:
:$\ds p = \prod_{n \mathop = 1}^\infty a_n$
The sequence $\sequence {p_N}$ defined as:
:$\ds p_N: = \prod_{n \mathop = 1}^N a_n = a_1 \cdot a_2 \cdots a_N$
is the '''sequence of partial products''' of the infinite product $\ds p = \prod_{n \mathop = 1}^\infty a_n$.
\end{definition}