Its impossible now Ive had time to think it out. The two conditions for a limit of infinity is that a. each iteration must be breater than the last, b. the DIFFERENCE must be monotonically non-decreasing.
Now, assume that a > 1. let n be the nth iteration. for n = 1, n > 1 obviously, so n^n > n.
for n = k, the kth iteration = n, the k+1th iteration = n^a, the difference = n^a-n.
for n = k+1, the k+1th iteration = n^a, the k+2th iteration = (n^a)^a, the difference = ((n^a)^a-n^a)
now, we must prove that ((n^a)^a-n^a) > n^a-n for all a > 1.
uh, my brain is too tired to proceed from here but thats essentially what you have to prove.
Anyway. QED proof ny mathematical Induction.
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