1. ## Geometric Variance Proof

Hi,
I'm a student in South-East Indiana, enrolled in a AP Stats class.
Our teacher has asked us to prove the geometric variance equation (the first equation pictured) USING ALGEBRA ONLY.
I've gotten it down to the 2nd equation and now I'm stuck, I've called MANY homework help lines and none can help.
It's due March 12th, next Wednesday, so I have about a week.
Please, your my last resort, give me a hint! (or even better, complete it for me )

He hinted it has something to do with infinity, and something called Zeno's Paradox, and I've googled Zeno's Paradox but all I've been able to find is about motion not existing.

Note: No calculus is to be used, this class is a pre-req for calculus.

Thanks for the help

2. Originally Posted by Distressed Student
Hi,
I'm a student in South-East Indiana, enrolled in a AP Stats class.
Our teacher has asked us to prove the geometric variance equation (the first equation pictured) USING ALGEBRA ONLY.
I've gotten it down to the 2nd equation and now I'm stuck, I've called MANY homework help lines and none can help.
It's due March 12th, next Wednesday, so I have about a week.
Please, your my last resort, give me a hint! (or even better, complete it for me )

He hinted it has something to do with infinity, and something called Zeno's Paradox, and I've googled Zeno's Paradox but all I've been able to find is about motion not existing.

Note: No calculus is to be used, this class is a pre-req for calculus.

Thanks for the help
You want to find:

$
\sum_{r=1}^n (r-1/p)^2 p q^{r-1}=
p\sum_{r=1}^n r^2 q^{r-1}-2\sum_{r=1}^n r q^{r-1}+\frac{1}{p}\sum_{r=1}^n q^{r-1}
$

Now do you recognise the terms on the right hand side?

RonL