1. ## Geometric Series Formula

What is the rule for using the formula

Sn = a(1 - r to the power of n)/1 - r

Sn = a(r to the power of n - 1)/r - 1

I have been looking for this rule for a while in various text books and websites. Any help would be greatly appreciated.

2. Originally Posted by tco99123
What is the rule for using the formula

Sn = a(1 - r to the power of n)/1 - r

Sn = a(r to the power of n - 1)/r - 1

I have been looking for this rule for a while in various text books and websites. Any help would be greatly appreciated.
There is no difference and hence on rule, they are two ways of writing the same thing.

CB

3. Originally Posted by tco99123
What is the rule for using the formula

Sn = a(1 - r to the power of n)/1 - r

Sn = a(r to the power of n - 1)/r - 1

I have been looking for this rule for a while in various text books and websites. Any help would be greatly appreciated.
$\frac{a(1-r^n)}{1-r}= \frac{-a(r^n-1)}{-(r-1)}= \frac{-1}{-1}\frac{a(r^n-1)}{r-1}= \frac{a(r^n-1)}{r-1}$

They are exactly the same thing.

4. Don't you get different answers when you use a negative for r, as well as an odd number for n?

5. Originally Posted by tco99123
Don't you get different answers when you use a negative for r, as well as an odd number for n?
Substitute some concrete values of n and r into each and convince yourself that the answers you get are the same.

6. Originally Posted by tco99123
Don't you get different answers when you use a negative for r, as well as an odd number for n?
Only if you do it wrong!