[Math] Express the mathematical constant $e$ in terms of a limit that goes to zero.

Question

The mathematical expression of the mathematical constant $e$ in terms of a limit that goes to infinity is $$e = \lim\limits_{n\rightarrow \infty} \left(1+\frac{1}{n}\right)^n$$

But can we express the mathematical constant $e$ in terms of a limit that goes to zero; $e=\lim\limits_{n\rightarrow 0} …$?

Thank you.

(problem from book of Spivak)

Answer 1

Is this what you want? $$\lim_{n\to 0}(1+n)^{1/n}=e$$