題組內容

2. Suppose that $\{a_n\}$ is a sequence $a_1 = 1$ and $a_{n+1} = \sqrt{a_n + 2}$, $\forall n \in N$.

(1) \( (8\%) \) Prove that \( 1 \leq a_{n} \leq 2 \), and \( a_{n} \leq a_{n+1} \), \( \forall n \in N \).