Value of 'e'

[Deleted member 4993]

Here is a terse rational number that apporimates 'e' to the first
18,457,734,525,360,901,453,873,570 digits.

\(\displaystyle e \ \ = \ \ ~ \left (1 + 9^{{-4}^{7\cdot 6}}\right )^{3^{2^{85}}}}\)

reference

http://farm2.static.flickr.com/1062/460 ... 5fcf_o.png

 

[BigGlenntheHeavy]

\(\displaystyle In \ many \ applications, \ it \ is \ important \ to \ have \ an \ approximation \ for \ n! \ when \ n \ is \ large.\)

\(\displaystyle A \ good \ approximation \ for \ n! \ is \ Stirling's \ Formula, \ to \ wit:\)

\(\displaystyle n! \ = \ \sqrt{2\pi n}\bigg(\frac{n}{e}\bigg)^n.\)