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!
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!
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.