1
vote
1answer
226 views

Find $N$, in the decimal expansion of the large number $N=4^{4^{4^4}}$

Find $N$, in the decimal expansion of the large number $$N=4^{4^{4^4}}$$ Following on from the question I posted yesterday about finding the number of digits ( Find the number of digits, $D$, in ...
2
votes
3answers
429 views

Find the number of digits, $D$, in the decimal expansion of the large number $N=4^{4^{4^{4}}}$

The full question is: Find the number of digits, $D$, in the decimal expansion of the large number $$N=4^{4^{4^{4}}}$$ Try and find the most efficient ways of finding $D$. I know that ...
4
votes
1answer
243 views

Definite integral of tetration between $0$ and $1$

In my old writes I found next formula, where is ${_{}^2}x$ is tetration: $$\int_0^1 {_{}^2}x \ dx = \sum\limits_{i=1}^\infty \frac {(-1)^{i+1}} {{_{}^2}i} \approx 0.783430511\ldots$$ And now I am ...
8
votes
0answers
195 views

Largest $x$ such that the power tower (tetration) $x^{x^{x^{x^{…}}}}$ converges? [duplicate]

Possible Duplicate: Infinite tetration, convergence radius Recently in this thread, Pseudo Proofs that are intuitively reasonable, I learned that ...