1
$\begingroup$

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 the decimal expansion of the large number $N=4^{4^{4^{4}}}$ )

I now wanted to find the $N$ (decimal expansion itself).

could I use this formula possibly?

$$ \sum_{i=1}^\infty 10^{-i} d_i $$

I wanted to work out $N$ because I was faced with the next part of the question

Say a robot could type $10$ billion digits a second! Find the time $T_n$, in years to type out the number $N$ in the previous part of this question.

I don't know how to go about calculating this..

any help is appreciated :)

  • 2
    What exactly is the question? Not the number of digits? Because the "next part of the question" seems to be related only to the number of digits.2012-12-28
  • 0
    the question now is ''Say a robot could type 10 billion digits a second! Find the time Tn, in years to type out the number N in the previous part of this question.'' but obviously to solve this problem N needs to be found which is the decimal expansion of 4^4^4^4. The number of digits was the first part of this entire question which is now done with. :)2012-12-28
  • 0
    I took a shot at tex-ing the formula, but I was reluctant to guess at the weird characters that are rendering on my screen. Hopefully someone can finish it off!2012-12-28
  • 3
    @Anonaanon Huh? Can't you answer that question by knowing how many digits it has? Divide by 10 billion to get the number of seconds, divide by 60 to get the number of minutes, etc.2012-12-28
  • 0
    yep, done! thank you :)2012-12-28

1 Answers 1