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

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)

• Do you $$\lim_{x\to a}f(x)=\lim_{h\to\frac1a}f\left(\frac1h\right)$$? – lab bhattacharjee Dec 30 '13 at 15:02

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