A sequence {an) is given by the recurrence relation a_{1}=\sqrt{2}, \quad a_{n+1}=\sqrt{2+a_{n}}, \quad \forall n \in \mathbb{N} (10 pts) By mathematical induction, show that {an} is non decreasing and bounded

above by 2. Deduce that {an} is a convergent sequence \text { Calculate } \lim _{n \rightarrow+\infty} a_{n}