A sequence is defined by a1=2, an+1=(2an+1)1/2
I have proven by induction that an is bounded above by 1+(2)1/2, and that an 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?