- #1
playboy
Homework Statement
Let [itex]a_{0} = a >1 [/itex] and let [itex]a_{n+1} = a^{a_n}[/itex].
Show that {[itex] a_{n} [/itex]} comverges for [itex] a < e^{e^-1} = 1.4446678 [/itex]
Homework Equations
This is a Theorm I learned in Real Analysis and hope to apply it to this problem:
Theorm: If a sequence is montonically increasing and bounded, then it is convergent
The Attempt at a Solution
{[itex] a_{n} [/itex]} = {[itex]a, a^a, a^{a^a}, ...[/itex]}
Clearly, {[itex] a_{n} [/itex]} is monotonically increasing is is bounded below by a.
How do I show that it is bounded above?
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