Exercise 4, § 7

Let $(a_n)$ be any sequence of finite real numbers $\geq 0$. Show that the sequence $\left( \frac{a_n}{(1 + a_1)(1 + a_2) \ldots (1 + a_n)} \right)$ is summable in $\mathbf{R}$ (express each term of this sequence as a difference).