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Factorial and summation.

  1. Sep 25, 2007 #1
    Hello all! In solving some math problems, I encountered the following sum:

    [tex]\sum_{k=1}^{r+1} kb \frac{r!}{(r-k+1)!} \frac{(b+r-k)!}{(b+r)!}. \quad \mbox{(eqn.1)}[/tex]

    Now, I have asked Maple to calculate the above sum for me, and the answer takes a very simple form:

    [tex]\frac{b+r+1}{b+1}. \quad \mbox{(eqn.2)}[/tex]

    My question is, does anyone know how to go from (eqn.1) to (eqn.2)? I am really bad at working with factorials, and so far I am not getting close. Maybe there are some results and properties of factorials and summation that can be used to simplify the above?
  2. jcsd
  3. Sep 25, 2007 #2


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    I suggest assuming specific values for b, r, k.
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