sequences and series - Studying the convergence of $U_{n+1} = sqrt{1 + U_n}$

How to can I study the convergence of $\begin{cases} U_0 \geqslant -1 \\ \forall n \in \mathbb{N}, U_{n+1} = \sqrt{1 + U_n} \end{cases}$ ?

My try to find the general term using Newton's method was for naught.