The Binomial Series

The binomial theorem

For a positive integer $n$: $$(a+b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r$$ where $\binom{n}{r} = \frac{n!}{r!(n-r)!}$ are the binomial coefficients (Pascal's triangle for small $n$).