Define sequence $s_1 = \sqrt{2}$ and $s_{n+1} = \sqrt{2+s_n}$. Find $\lim_{n \rightarrow \infty} s_n$ and prove this convergence.
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$