Hey.

I have recursive series:

$\forall n \in \mathbb{N}, \ \ a_{n+1}=\sqrt{2+a_n}, \ \ a_1=t, \ \ -2\leq t \in\mathbb{R}$

Prove:

If $-2\leq t\leq 2$ then A(n) is defined to every natural n and the series A(n) is an increasing monotonic series and is bounded above.

We have studied the material so far up to Cantor's lemma, but I don't know how to start here.

I have begun by trying to prove that this series is at least an increasing-monotonic but I got that this inequality has to be true:

$a_n^2<2+a_n$

Which I don't know how to confirm.

As to bounded above, have no idea how to think here on bounds...

Thanks.