why (1+h)^(1/h) = e ?

Question

I got it from the book
(1+h)^(1/h) = e = 2.71...
However, I don't know why we have that number ?

Answer 1

the actual definition of e is the limit as h aproaches infinity of (1+1/n)^n

you get 1 if you "just insert" infinity, but that's not what a limit (mathematics) means. It means that you let n approach infinity, and consider what happens when it gets arbitrarily large. Try it for increasing n:
(1+1/1)1 = 2
(1+1/2)2 = 2.25
(1+1/3)3 = 2.37...
(1+1/4)4 = 2.44...
(1+1/5)5 = 2.49...
(1+1/6)6 = 2.52...
This sequence gives results arbitrarily close to e.

Answer 2

don't ask... just know...