Let x1 = √2, xn+1 = √(2+xn). Use mathematical induction to show that xn < xn+1. Next show that if xn ≥ 2, then xn-1 ≥ 2 also. How do you conclude from this that xn ≤ 2 for all n? State why lim xn exists, and find the limit.
Upper bounds, limits, etc.
The Attempt at a Solution
I've done everything up to the point of "find the limit." Help?