In my book, it says that the(adsbygoogle = window.adsbygoogle || []).push({}); Binomial Seriesis

[tex]\sum_{n=0}^{\infty }\binom{n}{r} x^n[/tex]

Where [tex]\binom{n}{r} = \frac{n(n-1)...(n-r+1)}{n!}[/tex] for [tex]r\geq1[/tex] and [tex]\binom{n}{0} = 1[/tex]

Now here is where it got to be, I know that the [tex]\binom{n}{r} = \frac{n(n-1)...(n-r+1)}{n!}[/tex] were derived through the power series, but how does it explained the original statement that [tex]\sum_{n=0}^{\infty }\binom{n}{r} x^n[/tex]?

Since [tex]\binom{n}{r}[/tex] does not actually change. I mean it is still [tex]\frac{n!}{(n-r)!r!}[/tex] and so how can you put negative n into n!?

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# Binomial series vs Binomial theorem, scratching my head for three days on this

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