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I thought this might be an interesting question to ask, consider the following series

[tex]\sum_{n=0}^{\infty}\left(\begin{array}{cc}\alpha\\n \end{array}\right)x^{n}=(1+x)^{\alpha}[/tex]

this is known as the binomial series, whats confusing me is that how could this series exist when [tex]\alpha< n[/tex] especially when its a series that adds infinitely

number of terms, from my understanding this [tex]\left(\begin{array}{cc}\alpha\\n \end{array}\right)[/tex] can only be evaluated when [tex]\alpha>n[/tex] please help

thanxs

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# Binomial series

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