Evaluate: $$\lim_{n \to \infty}[(1+\frac{1}{n})^n-(1+\frac{1}{n})]^{-n}$$
attemp: Take $P=\lim_{n \to \infty}[(1+\frac{1}{n})^n-(1+\frac{1}{n})]^{-n}$ . Then taking log both side .$$\ln P=-\lim_{n \to \infty}n\ln [(1+\frac{1}{n})^n-(1+\frac{1}{n})]$$.Then stuck. Please help.