Limit of The Tower 2

Calculus Level 5

a 0 = a and a n + 1 = a a n a_0=a \mbox{ and } a_{n+1}=a^{a_n}

What is the smallest a > 0 a{>}0 such that a n a_n is convergent? (You might want to look at this problem first.)


The answer is 0.06598803584.

Peter Csorba by Peter Csorba , 45, Hungary

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1 solution

Parth Sankhe
Oct 25, 2018

The largest such a = e 1 e a=e^{\frac {1}{e}} , and the smallest such a = ( 1 e ) e a= (\frac {1}{e})^e .

0 Helpful 0 Interesting 0 Brilliant 1 Confused

i did the same thing. we have to understand the behaviour of the function a^x for x>0.

Srikanth Tupurani - 1 year, 10 months ago

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