Apologies if this has been asked before, I could not find it.
Define a sequence $a_n$ by $a_0 = 1$ and $a_n = 1+\sqrt{a_{n-1}}.$ Find the closed form, if it exists, of $a_n.$
So I can see this is just continued square roots. I know how to evaluate $$1+\sqrt{1+\sqrt{\cdots}}$$ to infinity, but i'm not sure how to evaluate for a finite amount of radicals. I have tried using the same method and considering the polynomial of which it is a root of, but none of these seemingly lead anywhere.
Also, if this could be generalized that would be helpful.