[jay_shark]

By definition e is the limit of (1+1/n)^n as n approaches infinity .

Try this out yourself .

Plug a large number for n in your calculator and you'll ~ match the number e you get on your calculator .

If we expand this using the binomial theorem we can represent as a limit of infinite sums .

e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! +....
e ~ 2.718281828....

e is an irrational number much like pi so it cannot be represented as a fraction a/b . There are many interesting properties about e but it's probably worthwhile to start with the definition before you get into other topics .