The number e=2.718281828 is the base of the natural log.
occurs in many areas of maths, and there are many methods to calculate it. One such is as the limit of the sequence
as
tends to infinity.
|
n |
\[(1 + 1/n)^n\]
|
|
1 |
2 |
|
2 |
2.25 |
|
3 |
2.370370370 |
|
4 |
2.44140625 |
|
10 |
2.593742460 |
|
100 |
2.704813829 |
|
1000 |
2.716923932 |
|
10000 |
2.718145927 |
|
100000 |
2.718268237 |
The table shows that asgets largergets closer to
We can write
Write
where
is a fixed number.
so that as n tends to infinity
The solution to this differential equation is
so put
to obtain