BINO::-

find-\sum_{r=0}^{q}({^{q}C_{r}}).(^{N}C_{n-r}).(a^{N-n+r}) ???

2 Answers

62
Lokesh Verma ·

\begin{pmatrix} q\\ r \end{pmatrix} \times \begin{pmatrix} N\\ n-r \end{pmatrix} \times a^{N-n+r} \\\text{Coefficient of }x^{N-n+q} \text{ in the expansion of } \\(1+x)^q\times (1+ax)^N

But then how does this help!
tried to cook up some binomial logic but that does not lead me anywhere either! [2]

341
Hari Shankar ·

Two constants there N and n. In fact you could just put N-n = m and reduce it to one constant. So I presume its a typo.

I've seen this prob posted in goiit and then in mathlinks where too there have been no responses.

So this thread may need the tag RIP :D

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