does any one knows how to prove that lim(1+1/n)^n=e when n goes to zero.
I will present this proof for what it's worth. Though, the posters proof builds
from this. This proof builds on the differentiability of ln(x). To be more exact
derivative of ln(x) at x=1.
Using the definition of a derivative, since 1/x=1, we get:
Therefore, it follows that:
from the continuity of can be written this way:
Now, we recognize this limit. The others play off it.
merely let .
This changes the limit to and we have said limit.