Problem

Source: New Zealand NZMOC Camp Selection Problems 2010 Seniors 1

Tags: recurrence relation, Sequence, algebra



For any two positive real numbers $x_0 > 0$, $x_1 > 0$, a sequence of real numbers is defined recursively by $$x_{n+1} =\frac{4 \max\{x_n, 4\}}{x_{n-1}}$$for $n \ge 1$. Find $x_{2010}$.