Skip to main content

Negative Binomial Series

โˆ‘j=0โˆž(j+kโˆ’1kโˆ’1)aj=(1โˆ’a)โˆ’kย ifย โˆฃaโˆฃ<1\sum\limits_{j=0}^{\infty} {{j+k-1} \choose {k-1}} a^j = (1-a)^{-k} ~\text{if}~ |a| < 1