I don't understand how to show that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lim_{n \rightarrow \infty} \left(1-\frac{a}{n} \left)^{n} = e^{-a} \ \ \forall a \in \mathbb{R}[/tex]

For exemple, if I say "Let x be the real number such that [itex]n=-ax \Leftrightarrow x=-n/a[/itex]. Then the limit is equivalent to

[tex]\lim_{-ax \rightarrow \infty} \left(1+\frac{1}{x} \right)^{-ax} = \left(\lim_{-ax \rightarrow \infty} \left(1+\frac{1}{x} \right)^{x} \right)^{-a}[/tex]

"but [itex]-ax \rightarrow \infty[/itex] is not equivalent to [itex]x \rightarrow \infty[/itex], so I can't conclude that the limit is [itex]e^{-a}[/itex].

What am I missing here ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limit is equivalent

**Physics Forums | Science Articles, Homework Help, Discussion**