How close can you get to the mathematical constant
e using the digits 0,1,2,3,4,5,6,7,8, and 9 each exactly once and the operations of addition, subtraction, multiplication, division, exponentiation, brackets and digit concatenation, in any order ?
Rem: no factorials, log, et al allowed.
One well known expression for e is lim {x to inf} (1+1/x)^x.
I tried to mimic that form with e ~= (1+2/(975-3))^486 = 2.7155, that is only 2 places after the decimal point.
It turns out that it is possible to do so much better with this method. In 2004 Richard Sabey found (1+9^-(4^(7*6)))^3^(2^85), based from 9^(4^(7*6)) = 3^(2^85). This approximation is good for an amazing 18.45 septillion digits.
Solution using a Limit
