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How would I find the limit for:

$$\lim_{n\to\infty}\left(\frac{n-1}{n}\right)^n$$

I know it approaches $\frac{1}{e}$, but I have no idea how it works. Plus, why does: $$\lim_{n\to\infty}\left(\frac{n-x}{n}\right)^n=\frac{1}{e^x}$$

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    Have a look at this: http://math.stackexchange.com/questions/115863/lim-n-rightarrow-infty1-fracrnn-is-equal-to-er2012-03-27
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    How has $e$ been defined to you?2012-03-27
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    e = $\lim_{n\to\infty}{(\frac{n+1}{n})^n}$2012-03-27
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    Thanks for the information. And is $n$ an integer? I assume it is. Would you mind confirming?2012-03-27
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    Yup, $n$ is an integer.2012-03-27
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    @user27251: Thanks.2012-03-27
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    @user27251 Hint: $\frac{n-1}n = \frac 1{\frac n{n-1}}$2012-03-27

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