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Okay and for fractional powers there is another version of the binomial theorem. The first thing to notice is that the rth binomial coefficient can be written as
(n(n-1)(n-2)(n-3)...(n-r+1))/r!
So if instead of nCk you use the above formula for the binomial coefficients you will end up with an infinite binomial series for any power.

Here's an example. Consider (1-x)-1. Its easy to show using the above expression for the binomial coefficients(with n = -1) that the series expansion here is
1+x+x2+x3 + .....

Of course this form of the theorem cannot be proved by induction. The Taylor's Theorem could be used though.