proof of this:

x^x^x^.^.^. (infinite exponentiation) only converges for e^(-e)<x<e^(1/e)

Please halp, for it is beyond me :(.

>>1
Man, that is fucking PhD math. GFTO.
Along with doing any root/ratio test, you'd also have to prove that when doing so, dividing an infinite series by a term is valid. And /that/ is the hard part.