(1) `g ` is discrete sine the inputs are natural numbers (1,2,3,...)

(2) `g(n)=.1(2)^(n-1) ` for `n in NN `

This is a geometric sequence with initial value 0.1 and constant ratio `r=2 ` .

(3) After 8 folds the stack is `.1(2)^7=12.8"mm" ` **

(4) If it were possible we can set up the equation:

`.1(2)^(n-1)=3.8"x"10^(11) ` (converting 380000km to mm)

`(2)^(n-1)=3.8"x"10^12 `

`(n-1)ln(2)=ln(3.8"x"10^12) `

`n-1~~41.789 `

(If you do not know logarithms, you could use guess and check to find that n=42 gives a height of approximately 220000km while n=43 gives a height of approximately 440000km.)

So n is approximately 43 folds.**

** There is a limiting factor given the initial thickness of the paper regardless of the size of the paper. This was discovered and proven by a high school student in 2001. See the link.

Also 51 folds will get you to the sun -- if it were physically possible.

**Further Reading**