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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.

  • 0
    Do you know what $\displaystyle\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n$ is?2012-12-21
  • 1
    yes.It is equal to **e**.2012-12-21

2 Answers 2