One more Power Tower

Calculus Level 5

Consider the infinite power tower \[\huge a^{a^{a^{\cdot^{\cdot^\cdot}}}}\]

with \(a=0.05\), representing the sequence \(x_1=a\) and \(x_{n+1}=a^{x_n}\). Find \(\displaystyle L=\lim_{n\to\infty}x_{2n}\).

Feel free to use a computer for some of your work.

Bonus Question: What about \(\displaystyle \lim_{n\to\infty}x_{2n+1}\)?

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