Euler's Number \( e \)

Euler's number \( e \approx 2.71828... \) is one of the most important constants in mathematics. Below are two classic algorithms to calculate it.

1. Limit Definition Method

\( e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n \)

Choose \( n \) (larger = more accurate):

\( e = \sum_{k=0}^{\infty} \frac{1}{k!} = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \dots \)

Number of terms:

Accepted value of \( e \):

2.718281828459045...