I'm given $a_{n+1}=a_n+\sqrt{1+a_n^2}$ along with $a_1=1$.
I'm not even sure if the general term has a nice formula. I tried the usual methods and substitutions with no luck. I suspect that if this sequence has a closed form formula, then it will involve something like complex numbers or some trig substitution.
Any idea? Is there a general rule for solving such recurrences?
