Question 68
Let $\alpha$ be an irrational number. For any $n \in \mathbb{N}^*$ let $a_n = \{n\alpha\}$ and define the sequence $(x_n)_{n \ge 1}$ by $x_n = (a_2 - a_1)(a_3 - a_2) \cdots (a_{n+1} - a_n)$. Show that the sequence is convergent and find its limit.