the expression posted is very good approximation of e^{3}
One sec, there is always a simple explanation. First consider this.
(1 + 1/1)^1 = 1.
(1 + 1/2)^2 = 9/4 = 2.25.
(1 + 1/3)^3 = 64/27 = 2.37
(1 + 1/4)^4 = 625/256 = 2.44
as you can see, the values are approaching something, right. For higher values of n, the expression (1 + 1/n)^n likely, remains constant with little variation. Similarly, use a calculator or some math programs and work out what he is saying, you will see the point.
Salahuddin
Maths online