Probability: Infinite Convergent Series and Random Variables

ZellDincht100

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?

tiny-tim

Hi ZellDincht100!
Yes it is …

[6/(k+4) - 6/(k+3)] - [6/(k+3) - 6/(k+2)]

ZellDincht100

Ahhhh I see! :D

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