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Math Help - Really weird limit

  1. #1
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    Really weird limit

    Hello, I need to show that \lim \limits_{n \to \infty } \frac{n!}{{n^n }} = 0 I have no idea how to approach this.

    Thanks in advance
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  2. #2
    o_O
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    \lim_{n \to \infty} \frac{n!}{n^{n}} = \lim_{n \to \infty} \frac{1 \cdot 2 \cdot \ \cdots \ \cdot (n-1)(n)}{\underbrace{n \cdot n \cdot \ \cdots \ \cdot n}_{n \text{ times}}} = \lim_{n \to \infty} \left( \frac{1}{n} \cdot \frac{2}{n} \cdot \ \cdots  \ \cdot \frac{n-1}{n} \cdot \frac{n}{n}\right) = \hdots
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