#math/calculus 

$|x|<1$
$\left(\begin{array}{l}\alpha \\ k\end{array}\right)=\frac{\alpha !}{k !(\alpha-k) !}$
$\begin{aligned}(1+x)^{\alpha} &=\sum_{k=0}^{\infty}\left(\begin{array}{l}\alpha \\ k\end{array}\right) x^{k} \\ &=1+\alpha x+\frac{\alpha(\alpha-1)}{2 !} x^{2}+\frac{\alpha(\alpha-1)(\alpha-2)}{3 !} x^{3}+\cdots, \end{aligned}$

[Binomial series - Wikipedia](https://en.wikipedia.org/wiki/Binomial_series#math_1)