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Negative Binomial Series

Negative Binomial Series

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∑j=0∞(j+k−1k−1)aj=(1−a)−k if ∣a∣<1\sum\limits_{j=0}^{\infty} {{j+k-1} \choose {k-1}} a^j = (1-a)^{-k} ~\text{if}~ |a| < 1
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