Sunday, 3 March 2013

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


Question: How do you prove\sum\limits_{s}\binom{n+s}{k+l}\binom ks\binom ls=\binom nk\binom nl





I'm just not sure where to begin. I tried writing both sides as the coefficient of x^n 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?

No comments:

Post a Comment

real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

How to find \lim_{h\rightarrow 0}\frac{\sin(ha)}{h} without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...