# Limit $\lim_{x \to \infty}\left (1- \frac1x\right)^x = ?$

$$\lim_{x \to \infty} \left(1+ \frac1x\right)^x = e$$ , then$$\lim_{x \to \infty} \left(1- \frac1x\right)^x =\; ?$$

I tried $\lim_{x \to \infty} \left(1- \frac1x\right)^x = \lim_{x \to \infty}\left(\frac{x-1}{x}\right)^x$, but this is not helpful.

• Well, $1-\frac1x=1+\frac{(-1)}{x}$. Does this help you? May 22 '18 at 2:29