1. ## Geometric series.

$\displaystyle \sum^n _{k=1} \pi^k-3 =[\pi^n-1][\pi-1]^{-1}-3n$ correct?

The back of my book is saying: $\displaystyle \sum^n _{k=1} \pi^k-3 =\pi[\pi^n-1][\pi-1]^{-1}-3n$ however, I am not really seeing where the pi is coming from. Suggestions?

2. Originally Posted by quantoembryo
$\displaystyle \sum^n _{k=1} \pi^k-3 =[\pi^n-1][\pi-1]^{-1}-3n$ correct?

The back of my book is saying: $\displaystyle sum^n _{k=1} \pi^k-3 =\pi[\pi^n-1][\pi-1]^{-1}-3n$ however, I am not really seeing where the pi is coming from. Suggestions?
Dear quantoembryo,

It is because the summation is takan from k=1.

$\displaystyle \displaystyle\sum_{k=0}^{k=n}r^k=\frac{1-r^n}{1-r}$

But, $\displaystyle \displaystyle\sum_{k=1}^{k=n}r^k=\frac{r(1-r^n)}{1-r}$

3. Originally Posted by quantoembryo
$\displaystyle \sum^n _{k=1} \pi^k-3 =[\pi^n-1][\pi-1]^{-1}-3n$ correct?

The back of my book is saying: $\displaystyle \sum^n _{k=1} \pi^k-3 =\pi[\pi^n-1][\pi-1]^{-1}-3n$ however, I am not really seeing where the pi is coming from. Suggestions?
You are using an incorrect formula for the sum of a geometric series. I suggest you go back and carefully review the correct formula (and also paying attention to the fact that you're sumiing from k = 1 not k = 0).

4. Thanks for the help, I figured it out