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e as a pandigital expression (Posted on 2017-04-23) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution using a Limit | Comment 1 of 2
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.

This impressive formula is the first entry on Mathworld's page of e approximations http://mathworld.wolfram.com/eApproximations.html

Mathmagic covers more approximations http://www2.stetson.edu/~efriedma/mathmagic/0804.html

  Posted by Brian Smith on 2017-04-23 12:46:45
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