Definition:Absolute Convergence of Product/General Definition/Definition 2

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Definition

Let $\struct {\mathbb K, \norm {\,\cdot\,} }$ be a valued field.

Let $\sequence {a_n}$ be a sequence in $\mathbb K$.


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