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 sequenceastends 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 toWe can write
Writewhereis a fixed number.
so that as n tends to infinityThe solution to this differential equation isso putto obtain