# How was e computed?

1. Feb 24, 2004

### Matt Jacques

How was "e" computed?

The title says it all.

2. Feb 24, 2004

3. Jul 23, 2004

### mathwonk

the number e is by definition the number e such that the integral of 1/x from 1 to e equals 1. thus any method of approximating integrals allows you to approximate e. i.e. if yuo show that the integral of 1/x from 1 to 2.7 is less than 1 you have shown that e is greater than 2.7

another nice way is to use the taylor series for e^x, and plug in x =1, which gives e = the limit of the series 1 + 1/2 + 1/6 + 1/24 + 1/120 + ....+ 1/n!+....

My freshman calc prof gave as an exercise to prove this way that e starts out as 2.718281828.... but i never completed it. i could not believe in those days that math took that much work!

4. Jul 23, 2004

### eJavier

calculate $$\lim_{n\to\infty} (1+\frac{1}{n})^n$$