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Math Help - Geometric Series Formula

  1. #1
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    Geometric Series Formula

    What is the rule for using the formula

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

    Instead of

    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.
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  2. #2
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    Quote Originally Posted by tco99123 View Post
    What is the rule for using the formula

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

    Instead of

    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
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  3. #3
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    Quote Originally Posted by tco99123 View Post
    What is the rule for using the formula

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

    Instead of

    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.
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  4. #4
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    Don't you get different answers when you use a negative for r, as well as an odd number for n?
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  5. #5
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    Quote Originally Posted by tco99123 View Post
    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.
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  6. #6
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    Quote Originally Posted by tco99123 View Post
    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!
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