Endless fun with power towers

Calculus Level 3

For a=116a=\dfrac1{16}, consider the (finite) power tower,

xn=aaaa2n  a’s\Large x_n=\underbrace{a^{a^{\cdot^{\cdot^{a^a}}}}}_{2n \; a\text{'s}}

For example, x1=aax_1=a^a and x2=aaaax_2=a^{a^{a^a}}.

Find limnxn\displaystyle \lim_{n\to\infty}x_n, to three significant figures.

Bonus What happens if we consider a power tower with an odd number of aa's?

×

Problem Loading...

Note Loading...

Set Loading...