J. Let $a_0$ and $a_1$ be positive real numbers, and set $a_{n+2} = \sqrt{a_{n+1} + \sqrt{a_n}}$ for $n \ge 0$.
(a) Show that there is $N$ such that for all $n \ge N$, $a_n \ge 1$.
(b) Let $\epsilon_n = |a_n - 4|$. Show that $\epsilon_{n+2} \le (\epsilon_{n+1} + \epsilon_n)/3$ for $n \ge N$.
(c) Prove that this sequence converges.