Absolutely Convergent Product Does not Diverge to Zero

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 it is not divergent to $0$.

Also see

 * Absolutely Convergent Product is Convergent