Factors in Absolutely Convergent Product Converge to One/Proof 2

Proof
We have that $\ds \prod_{n \mathop = 1}^\infty \paren {1 + a_n}$ is absolutely convergent.

Hence the real product $\ds \prod_{n \mathop = 1}^\infty \paren {1 + \norm {a_n} }$ is convergent.

By Factors in Convergent Product Converge to One:
 * $\norm {a_n} \to 0$.

Thus:
 * $a_n \to 0$