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[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 ?

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# Limit is equivalent

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