Part II : Give the detailed calculation or proof process of the following questions.

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 \(a_{n} \leq a_{n+1}\), \(\forall n \in N\).