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:

$$\Sigma$$ $$12/(k+4)(k+3)(k+2)$$

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?

 

[tiny-tim]

Hi 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)] ​

 

[ZellDincht100]

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..