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

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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)

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1 Answer

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

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