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        riddles >> general problem-solving / chatting / whatever >> Messy sum of sums
        
(Message started by: jarls on Aug 30^th, 2009, 12:23am)

Title: Messy sum of sums
Post by jarls on Aug 30^th, 2009, 12:23am

Why does this turn out to be a fraction (not just for displayed values)?

Title: Re: Messy sum of sums
Post by towr on Aug 30^th, 2009, 1:33am

Because you're adding a finite number of rational numbers.

Title: Re: Messy sum of sums
Post by Obob on Aug 30^th, 2009, 5:21am

It seems to me you probably have an error in there, though. One of the terms is (d-(p-1))!, where the range p is evaluated over makes d-(p-1) negative most of the time. There is no good interpretation for the factorial of a negative number. This should raise a red flag, unless you are absolutely sure this is intended.

In fact, if it wasn't for the last term, you would get an integer for all positive integer inputs.

Title: Re: Messy sum of sums
Post by Eigenray on Sep 3^rd, 2009, 3:35pm

n! may not be defined for n a negative integer, but 1/n! can be taken to be 0; e.g., C(n,k) = n!/(k! (n-k)!) even if k<0 or k>n. The problem seems to be the k^d-l in the third sum: since l can be as large as d+3, you can get a denominator of k³.