Chapter 8.1, Problem 42E

A sequence {a_n} is given by $a_1=\sqrt{2},a_{n+1}=\sqrt{2+a_n}.$

(a) By induction or otherwise, show that {a_n} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim_n→∞ a_n. exists.

(b) Find lim_n→∞ a_n.