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

Definition

Let $\sequence {a_n}$ be a sequence of complex numbers.

The infinite product $\ds \prod_{n \mathop = 1}^\infty \paren {1 + a_n}$ is absolutely convergent if and only if the series $\ds \sum_{n \mathop = 1}^\infty a_n$ is absolutely convergent.

Also see

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