: e = 1/1! + 1/2! + 1/3! + 1/4! + ... |
: e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ... |
∞ e = ∑ (n!)-1 n=0
Here n! stands for the factorial of n.
The number e is relevant because one can show that the exponential function exp(x) can be written as ex; the exponential function is important because it is, up to multiplication by a scalar, the unique function which is its own derivative and is hence commonly used to model growth or decay processes.
The number e is known to be irrational and even transcendental. It features (along with a few other fundamental constants) in the most remarkable formula in the world.