Here's the weird limit:(adsbygoogle = window.adsbygoogle || []).push({});

lim n[itex]\rightarrow[/itex] [itex]\infty[/itex]_{a}C_{n}/n^{a}= 1/(a!)

Don't ask how I thought this up, but let me explain my reasoning.

Let's say that a=3. Then_{a}C_{n}= (n)(n-1)(n-2)

And because n is approaching infinity, could it be (n)(n)(n) = n^{3}?

I wouldn't normally think of things like this but if it's true then it helps me out.

The only thing is that (n)(n-1)(n-2)= n^{3}+something*n^{2}+something*n

And when I graphed it it looked like it approaches zero.

I've never learned limits formally. Thanks.

EDIT:_{a}C_{n}is a Choose n, or n!/(a![n-a]!)

EDIT: Wolfram alpha is amazing http://www.wolframalpha.com/input/?i=lim+(x!/(3!(x-3)!x^3))+as+x->+infinity

Sorry for not trying this before posting. I'd still be interested in other replies as to why this is true, though

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# Is this weird limit true?

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