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Problem of the Day #180: Infinite Power Towers September 15, 2011

Posted by Albert in : potd , trackback

$\def\iddots{{\kern3mu\raise1mu{.}\kern3mu\raise6mu{.}\kern3mu \raise12mu{.}}}$
What is the maximum value of $a$ for which $a^{a^{a^{\iddots}}}$ converges to a finite value? To what value does it converge?

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