So, I have been trying to solve this problem since last night and finally now decided to have some help , here. If -
$ y_1= \sqrt p$, $p> 0$, and $y_{n+1} = \sqrt{p+y_{n}}$ for all $n \in \mathbb{N}$. I wish to show that $y(n)$ converges and find its limit.
It requires use of monotone convergence theorem so we will have to prove that it is bounded and monotone, first.
I solved a question just like this one one I was given some real value of $p$ but with some unknown like $p$ here I don't know how to start with proving it to be bounded or monotone. I f somebody can just help me with that I would be truly grateful.