A sequence is defined by a_{1}=2, a_{n+1}=(2a_{n}+1)^{1/2 }I have proven by induction that a_{n}is bounded above by 1+(2)^{1/2}, and that a_{n}is monotone increasing. By the monotone convergence theorem I can deduce that the sequence converges but I cannot figure out how to prove what it converges to. I know that it converges to 1+(2)^{1/2}but I don't know how to show that. Could someone help me finish this question?