Definition:Absolute Convergence of Product/Complex Numbers/Definition 2

Definition
Let $(a_n)$ be a sequence of complex numbers.

The infinite product $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + a_n}\right)$ is absolutely convergent the series $\displaystyle \sum_{n \mathop = 1}^\infty a_n$ is absolutely convergent.

Also see

 * Equivalence of Definitions of Absolute Convergence of Product of Complex Numbers