1/(1-x)^k

The theory can be extended to negative numbers.

Look here:

< http://en.wikipedia.org/wiki/Binomial_coefficient#Generalization_to_negative_integers >

< http://mathworld.wolfram.com/BinomialCoefficient.html >

yes it is binomial, k is a positive integer.

Wiki has some information about negative binomials

http://en.wikipedia.org/wiki/Binomial_coefficient

if Bin(k,n) = k!/(n!(k-n)!

then

Bin(-k,n) =(-1)^n *k!/(n!(k-n)!

               = (-1)^n *Bin(k,n)

So for instance  

  1/(1-x) = 1+ x + x² + x³ + ....

To really understand why this is the case requires going beyond Pascal's triangle. These ideas are often presented without sufficient justification, in essence they are saying:- believe me it is true and it works.

The coefficients for -ve and fractional powers come from looking at the problem as a Taylor Series expansion.

Bin(k,n) = k!/(n!(k-n)!
Bin(-k,n) =(-1)^n *k!/(n!(k-n)!


Each has one paranthesis which don't have any mathcing paranthesis?
Can you fix it please @GwynforWeb ?