Question 98
The maximum of two real numbers $a$ and $b$ is defined as follows:
$$
\max\{a, b\} = \begin{cases} a, & \text{if } a \ge b, \\ b, & \text{otherwise.} \end{cases}
$$
For any two positive real numbers $x_0 \gt 0$, $x_1 \gt 0$ a sequence of real numbers $x_n$ is defined recursively as given below. Find $x_{2010}$.
$$
x_{n+1} = \frac{4 \max\{x_n, 4\}}{x_{n-1}} \quad \text{for } n \ge 1.
$$
$$
\max\{a, b\} = \begin{cases} a, & \text{if } a \ge b, \\ b, & \text{otherwise.} \end{cases}
$$
For any two positive real numbers $x_0 \gt 0$, $x_1 \gt 0$ a sequence of real numbers $x_n$ is defined recursively as given below. Find $x_{2010}$.
$$
x_{n+1} = \frac{4 \max\{x_n, 4\}}{x_{n-1}} \quad \text{for } n \ge 1.
$$