7.4: Summary

Last updated

Jul 12, 2021
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- 7.3: Using Generating Functions To Count Things
- 8: Generating Functions and Recursion

Joy Morris
University of Lethbridge

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If $n > 0$ is an integer, then

$\binom{−n}{r} = (−1)^r \binom{n + r − 1}{r}$ .

The Generalised Binomial Theorem
$1 + x + . . . + x^k = \dfrac{(1 − x^{k+1})}{(1 − x)}$
Using generating functions for counting things
Important Definitions:
- Generating function for a sequence
- Generalised binomial coefficient

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