Question 10
Let be given two positive real numbers $a_0$ and $a_1$. The sequence $(a_n)$ is defined by
$$
a_{n+2} = 1 + \frac{a_{n+1}}{a_n}, \quad n = 0,1,2,\ldots
$$
Prove that $|a_{2012} - 2| \lt 10^{-200}$.
$$
a_{n+2} = 1 + \frac{a_{n+1}}{a_n}, \quad n = 0,1,2,\ldots
$$
Prove that $|a_{2012} - 2| \lt 10^{-200}$.