Zurtex

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## Main Question or Discussion Point

I'm doing some tutoring tomorrow morning for a girl who needs to do some maths resits. I was looking through the papers and you need to prove that:

[tex]n^{n-1} \geq n! \quad \forall n > 1 \; \text{and} \; n \in \mathbb{N}[/tex]

Which is fine, but it asks to you to do it by proving by definition that:

[tex]\lim_{n \rightarrow \infty} \frac{n!}{n^n} = 0[/tex]

And I have to admit that I can't quite remember how to do this one, if someone could point me in the right direction that would be great, I remember seeing a proof for it so I'm sure it'll come back to me.

[tex]n^{n-1} \geq n! \quad \forall n > 1 \; \text{and} \; n \in \mathbb{N}[/tex]

Which is fine, but it asks to you to do it by proving by definition that:

[tex]\lim_{n \rightarrow \infty} \frac{n!}{n^n} = 0[/tex]

And I have to admit that I can't quite remember how to do this one, if someone could point me in the right direction that would be great, I remember seeing a proof for it so I'm sure it'll come back to me.