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I've been asked to compute the value of a sum. The answer should be an expression involving one or two binomial coefficients.

The initial expression:

$$ \sum_{k} \binom{80}{k} \binom{k+1}{31} $$

After many iterations, I think I'm still unable to answer the question appropriately. The following is my latest result:

$$ \binom{80}{30} \sum_{k=30}^{80} \binom{50}{80 - k} (k + 1) $$

How might I go about simplifying the remaining summation? Now that I've determined an exact range for k, do I just need to compute the value?

Bradford Fiser
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  • did you see this? http://math.stackexchange.com/questions/528900/how-do-i-compute-the-summation-of-80-choose-k-cdot-k1-choose-31 – Doc Oct 28 '13 at 13:04

0 Answers0