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Binomial Series Question

  1. Oct 6, 2006 #1
    How does one deduce the following:

    We are given

    [tex] \binom{-3}{n} = \frac{(-3)(-4)(-5)\cdot\cdot\cdot\cdot\cdot(-3-n+1)}{n!} = \frac{(-3)(-4)(-5)\cdot\cdot\cdot\cdot[-(n+2)]}{n!} [/tex]. How do we get from here to:

    [tex] \frac{(-1)^{n}\cdot2\cdot3\cdot4\cdot5\cdot\cdot\cdot\cdot(n+1)(n+2)}{2\cdot n!} = \frac{(-1)^{n}(n+1)(n+2)}{2} [/tex]?

    Last edited: Oct 6, 2006
  2. jcsd
  3. Oct 6, 2006 #2
    nevermind. I figured it out
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