I have a random variable problem. I need to prove that my equation I came up with is a valid probability mass function.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Probability: Infinite Convergent Series and Random Variables

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