e is the limit of (1 + 1/x)^x as x goes towards infinity.
Either you can use arbitrarily high numbers (the larger the number the better the approximation) or you can use a Taylor Series.
(Because the derivative of e^x is e^x, the Taylor Series is quite simple-
e = 1/0! + 1/1! + 1/2! + 1/3! + ….)