Solving $\lim_{n\to \infty} (\frac{n+1}{n})^n $

Question

$$\lim_{n\to \infty} \left(\frac{n+1}{n}\right)^n = e$$

I would like to know how to solve such a limit.

It's one of the definitions of $e$ – Alex May 05 '14 at 07:30 — Alex, May 05 '14 at 07:30
What is your definition of $e$? – Bonnaduck May 05 '14 at 07:42 — Bonnaduck, May 05 '14 at 07:42

score 4 · Accepted Answer · answered May 05 '14 at 07:34

4

The limit of $\left(\frac{n+1}{n}\right)^n$ is actually the first real definition of $e$. The standard practice is to show that the sequence is bounded from above and increasing, therefore the limit exists. The limit is then named $e$.

answered May 05 '14 at 07:34

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Solving $\lim_{n\to \infty} (\frac{n+1}{n})^n $

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