Factors in Absolutely Convergent Product Converge to One/Proof 1

Proof
Because $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + a_n}\right)$ is absolutely convergent, $\displaystyle \sum_{n \mathop = 1}^\infty a_n$ is absolutely convergent.

By Terms in Convergent Series Converge to Zero, $a_n\to0$.