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How can we show for any $\alpha\in\Bbb R$, the Maclaurin series of the function $p(x) := (1 + x)^\alpha$ is

$$1+\alpha x + \frac{\alpha(\alpha-1)}2+\ldots = \sum_{n = 0}^\infty \frac{\alpha(\alpha-1)(\alpha-2)\ldots(\alpha-n+1)}{n!} x^n\;?$$

I thought of using the binomial theorem, but that doesn't really do much help

Also, won't I need some induction argument?

Thanks for the help!

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