The value of e can be derived in a number of ways.
By definition, substituting a large number for x into (1 + 1/x)^x will give you an approximation.
Using a Taylor Series will give you =>
e = 1/0! + 1/1! + 1/2! + 1/3! ….
Obviously the more terms in the infinite series you use, the better the approximation.
(x! = x * (x – 1) * (x – 2) … * 3 * 2 * 1)