What is (2^0.5)^(2^0.5)^(2^0.5)...?
Your answer is
x^x^x^x^....if convergent, We have x=x^x , Lnx=xLnx, we get x=1,If x>1,It would be Divergent.
But I think it is wrong. From x^x^x... convergent, you cannot get x=x^x. Let's say x=.5. .5, .5^.5, .5^.5^.5,... is convergent because it is increase and smaller than 1^.5^.5..., which is 1. But you cannot say .5=.5^.5.
Since your reason is wrong, I am not sure that x^x^x^x^....is Divergent when x>1.