i dont know $-a$ in this equation really mean, explain it too please $$ \left(\begin{array}{c}a+m-1\\ m\end{array}\right) = (-1)^m \left(\begin{array}{c}-a\\ m\end{array}\right) $$
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Where did you get this problem from? What is the context? Are you working with some form of generalized binomial coefficient? Otherwise, unless $;a\le0;$, the equality's right hand makes no sense. – DonAntonio Dec 02 '19 at 18:50
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Look at https://en.wikipedia.org/wiki/Binomial_coefficient#Generalization_and_connection_to_the_binomial_series – copper.hat Dec 02 '19 at 18:51
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Possible duplicate of Negative binomial coefficient. See also this post. – Arthur Dec 02 '19 at 18:52
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It is used for the general expansion of $(1+x)^\alpha$. – copper.hat Dec 02 '19 at 18:52
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A generalized binomial coefficient $\binom{x}{m}$ with $m\in\mathbb N$ but $x$ not necessarily a natural number is given by $$\frac{x(x-1)\cdots (x-m+1)}{m!}$$ Can you use this to prove it?
Matt Samuel
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