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Probability: Infinite Convergent Series and Random Variables

  1. Feb 22, 2010 #1
    I have a random variable problem. I need to prove that my equation I came up with is a valid probability mass function.

    In the problem, I came up with this for my probability mass function:

    [tex]\Sigma[/tex] [tex]12/(k+4)(k+3)(k+2)[/tex]

    Maple says that this does in fact converge to 1, so it's valid; however...I can't use "Maple said so" as an answer.

    My attempt was to break it up using partial fraction decomposition:
    ([tex]6/(k+4)[/tex]) - ([tex]12/(k+3)[/tex]) + ([tex]6/(k+2)[/tex])

    I was hoping that this would be telescoping, but it is not. Does anyone have an idea on how I can prove that this converges to 1?
  2. jcsd
  3. Feb 23, 2010 #2


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    Hi ZellDincht100! :smile:
    Yes it is …

    [6/(k+4) - 6/(k+3)] - [6/(k+3) - 6/(k+2)] :wink:
  4. Feb 23, 2010 #3
    Ahhhh I see! :D

    Thanks! Dunno how I didn't see that before..
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