Is it possible to find a formula to expand this polynomial: [tex](n+1)(n+2)\ldots(n+x)[/tex] where [tex]n,x\in\textbf{N}[/tex]. In other words, is it possible to deduce a formula [tex]F[/tex] such that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\displaystyle\prod_{k=1}^x{(n+k)}=\displaystyle\sum_{LB}^{UB}F[/tex]

Where LB and UB are the respective lower and upper bounds. I'm assuming it has something to do with binomial coefficients since the obvious

[tex]{(a+b)}^n=\displaystyle\sum_{k=0}^{n}{\binom{n}{k}a^{n-k}b^{k}}[/tex]

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# Polynomial Expansion of a Constant and Variable

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