Definition:Sequence of Partial Products

Definition
Let $p$ be the infinite product:
 * $\displaystyle p = \prod_{n \mathop = 1}^\infty a_n$

The sequence $\sequence {p_N}$ defined as:
 * $\displaystyle p_N: = \prod_{n \mathop = 1}^N a_n = a_1 \cdot a_2 \cdots a_N$

is the sequence of partial products of the infinite product $\displaystyle p = \prod_{n \mathop = 1}^\infty a_n$.