Factors in Absolutely Convergent Product Converge to One

Theorem
Let $\mathbb K$ be a field with absolute value $\left\vert{\, \cdot \,}\right\vert$.

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

Then $a_n\to0$.

Also see

 * Factors in Convergent Product Converge to One
 * Absolutely Convergent Product is Convergent (which relies on this result)