Binomial Series
Binomial series are a special type of Power Series which are used to describe functions of the form $(a+x)^r$. Even though a power series can be calculated for every single form of this function, it is often easier to calculate the power series of $(1-x)^r$ which is
$$ \sum \binom{r}{n} x^n $$
Here, we use a Binomial Coefficient.
After knowing the power series for $(1-x)^r$, we can treat it as a function and derive any function in the form $(a+x)^r$.