Question 25
The first two terms of a sequence are $a_1 = 1$ and $a_2 = \dfrac{1}{\sqrt{3}}.$ For $n \ge 1,$ $$
a_{n+2} = \dfrac{a_n + a_{n+1}}{1 - a_n a_{n+1}}.
$$ What is $|a_{2009}|?$
a_{n+2} = \dfrac{a_n + a_{n+1}}{1 - a_n a_{n+1}}.
$$ What is $|a_{2009}|?$