Series

The binomial expansion

For a positive integer $n$,

$$(a + b)^n = a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \dots + b^n$$

where $\binom{n}{r} = \dfrac{n!}{r!(n-r)!}$ (the $\text{}^nC_r$ on your calculator). The general term in $(a+b)^n$ is $\binom{n}{r}a^{n-r}b^r$. The powers of $a$ decrease while the powers of $b$ increase, and each term's powers add to $n$.