Discuss the convergence of the sequence: $a=?iso-8859-1?Q?=5F1=3D1=2Ca=5F{n+1}=3D\sqrt{2+a=5Fn}_\quad_\forall_n_\in_?=\mathbb{N}$ – math.stackexchange.com

Discuss the convergence of the sequence: $a_1=1,a_{n+1}=\sqrt{2+a_n} \quad
\forall n \in \mathbb{N}$ – math.stackexchange.com

Computing the first few terms $$a_1=1,
a_2=\sqrt{3}=1.732....,a_3=1.9318....,a_4=1.9828...$$ I feel that
$(a_n)_{n\in \mathbb{N}}$ is bounded above by 2, although I have no
logical reasoning for this. …