Question 2
Let $a_{0} = \frac{6}{7}$, and
$$
a_{n+1} = \begin{cases}2 a_{n} & \text{ if } a_{n} \lt \frac{1}{2} \\ 2 a_{n} - 1 & \text{ if } a_{n} \geq \frac{1}{2}\end{cases}
$$
Find $a_{2008}$.
$$
a_{n+1} = \begin{cases}2 a_{n} & \text{ if } a_{n} \lt \frac{1}{2} \\ 2 a_{n} - 1 & \text{ if } a_{n} \geq \frac{1}{2}\end{cases}
$$
Find $a_{2008}$.