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Topic: Messy sum of sums (Read 475 times) |
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jarls
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Why does this turn out to be a fraction (not just for displayed values)?
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| « Last Edit: Aug 30th, 2009, 12:24am by jarls » |
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towr
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Re: Messy sum of sums
« Reply #1 on: Aug 30th, 2009, 1:33am » |
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Because you're adding a finite number of rational numbers.
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Obob
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Re: Messy sum of sums
« Reply #2 on: Aug 30th, 2009, 5:21am » |
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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.
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| « Last Edit: Aug 30th, 2009, 5:24am by Obob » |
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Eigenray
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Re: Messy sum of sums
« Reply #3 on: Sep 3rd, 2009, 3:35pm » |
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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 kd-l in the third sum: since l can be as large as d+3, you can get a denominator of k3.
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