The question
$x_{1} = \sqrt{2}$ and $x_{n+1} = \sqrt{2+x_{n}}$. Show that the sequence converges and find it's limit.
AttemptIf I assume that the limit exists, then I am able to find the limit. But how to show the existence in the first place. I tried to go along the direction to show that it is monotonic and bounded, but no manipulation could give any tangible path. Kindly help.