# Probability: Infinite Convergent Series and Random Variables

by ZellDincht100
Tags: convergent, infinite, probability, random, series, variables
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 P: 3 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: $$\Sigma$$ $$12/(k+4)(k+3)(k+2)$$ 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: ($$6/(k+4)$$) - ($$12/(k+3)$$) + ($$6/(k+2)$$) 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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P: 26,148
Hi ZellDincht100!
 Quote by ZellDincht100 My attempt was to break it up using partial fraction decomposition: ($$6/(k+4)$$) - ($$12/(k+3)$$) + ($$6/(k+2)$$) I was hoping that this would be telescoping, but it is not.
Yes it is …
[6/(k+4) - 6/(k+3)] - [6/(k+3) - 6/(k+2)]
P: 3
 Quote by tiny-tim Hi ZellDincht100! Yes it is … [6/(k+4) - 6/(k+3)] - [6/(k+3) - 6/(k+2)]
Ahhhh I see! :D

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

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