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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 :)

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    yep, done! thank you :)2012-12-28

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Given that you know approximately the number of digits $D$, and that there are about $3.16 \cdot 10^7$ seconds in a year, it would take $\frac D{3.16 \cdot 10^{17}}$ years

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    @Anonaanon: That is correct. It takes no more digits to write 99 than it does 11, so to know how long it takes to write you just need the number of digits.2012-12-28