
7.4: Summary


• 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