Let's go back to the original example which is A1=a=2^.5(about 1.4142) and An+1=a^An. (1)An is increase. (2)An<2
Proof of (2) by induction
A1=a<2
Assume An<2 then An+1=a^An <a^2=2.
Therefore An<2 for all n.
It shows An is bounded by 2. According the book, an increasing sequence that is bounded from above has a limit. Why do you think it diverges?
Thanks a lot.
