Could anyone please point me in the direction on how to proof $\displaystyle C(-n, k) = (-1)^k C(n + k - 1, k)$ ?

I'm having a problem with this as the factorial of a negative integer is infinit.

Thanks in advance!

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- Dec 22nd 2009, 08:45 AMchris2547Proof for an alternative binomial coefficient
Could anyone please point me in the direction on how to proof $\displaystyle C(-n, k) = (-1)^k C(n + k - 1, k)$ ?

I'm having a problem with this as the factorial of a negative integer is infinit.

Thanks in advance! - Dec 22nd 2009, 08:57 AMnovice
- Dec 22nd 2009, 09:10 AMchris2547
- Dec 22nd 2009, 09:27 AMCaptainBlack
- Dec 22nd 2009, 09:56 AMawkward
The starting point in this is to generalize the definition of C(x, k) to be

$\displaystyle C(x,k) = \frac{x (x-1) (x-2) \cdots (x-k+1)}{k!}$.

With this definition, x can be any real number, not necessarily an integer. k must be a non-negative integer.

Now let x = -n and see what you get. - Dec 22nd 2009, 10:04 AMchris2547