Sunday, 3 March 2013

summation - Proving this infinite sum of a product of three binomials: sumlimitssbinomn+sk+lbinomksbinomls=binomnkbinomnl


Question: How do you proves(n+sk+l)(ks)(ls)=(nk)(nl)





I'm just not sure where to begin. I tried writing both sides as the coefficient of xn of the expansion of a binomial. But obviously, that doesn't fit the right-hand side because it's the product of two binomials.



I'm guessing that we'll need the multinomial theorem. Is that correct? Do you have any other ideas?

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