Special Cases
If α is a nonnegative integer n, then the (n + 1)th term and all later terms in the series are 0, since each contains a factor (n − n); thus in this case the series is finite and gives the algebraic binomial formula.
The following variant holds for arbitrary complex β, but is especially useful for handling negative integer exponents in (1):
To prove it, substitute x = −z in (1) and apply a binomial coefficient identity.
Read more about this topic: Binomial Series
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