Section 12.3 Negative Binomial Series
\((a+b)^{-n} = \sum_{k=0}^{\infty} {\binom{-n}{k} a^k b^{-n-k}}\)
Theorem 12.3.1. Alternate Form for Negative Binomial Series.
\((a+b)^{-n} = \sum_{k=0}^{\infty} {(-1)^k \binom{n+k-1}{k} a^k b^{-n-k}}\)
\((a+b)^{-n} = \sum_{k=0}^{\infty} {\binom{-n}{k} a^k b^{-n-k}}\)
\((a+b)^{-n} = \sum_{k=0}^{\infty} {(-1)^k \binom{n+k-1}{k} a^k b^{-n-k}}\)