The above power tower can be viewed as a recurrence relation: for and .
It is known that is a constant and is the solution of the above equation. What is the largest range for ?
Inspiration and more inspiration .
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Here are the graphs showing iteration of a k for (i) n < 2 , (ii) 2 < n < 4 and (iii) n > 4 respectively.
We can get the idea from here that the k → ∞ lim a k = 2 for all n < 4 .
Any good algebraic proof?