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456 B
456 B
| title |
|---|
| binomial series |
#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}