# Geometric Series Formula

• Nov 7th 2008, 06:23 AM
tco99123
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.
• Nov 7th 2008, 06:31 AM
CaptainBlack
Quote:

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
• Nov 7th 2008, 09:45 AM
HallsofIvy
Quote:

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.
• Nov 7th 2008, 04:18 PM
tco99123
Don't you get different answers when you use a negative for r, as well as an odd number for n?
• Nov 7th 2008, 05:33 PM
mr fantastic
Quote:

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.
• Nov 8th 2008, 12:02 AM
HallsofIvy
Quote:

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!