Calculating the Limit of (1+1/n)^n as n Approaches Infinity

[Matt Jacques]

How was "e" computed?

The title says it all.

 

[cookiemonster]

There's lots of ways. Take your pick:

http://mathworld.wolfram.com/e.html

cookiemonster

 

[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!

 

[eJavier]

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