# 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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