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Math Help - Difficulty writing the summation notation..

  1. #1
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    Difficulty writing the summation notation..

    I'm having some difficulty writing the geometric summation notation of this question:

    3. a) write the series 10 + 5 + 5/2 + 5/4 + 5/8 + 5/16 + 5/32 using summation notation (sigma).

    I discovered each term is divided by 2 so in this case r= 1/2

    The formula Sn = [a(r^n-1)] / (r-1) should be this:

    S1 = [10 (1/2^2 - 1)] / (1/2 - 1)

    However, when I then try to verify this formula I get 10 when n=1 but 15 when n=2.

    I must be doing something wrong, but I don't know what. I will give this another crack and see if I can find my errors. Any help is appreciated.
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  2. #2
    Super Member
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    Hi

    You made one simple mistake only:

    The geometric sum is indeed  S_n = \frac{a(r^n-1)}{r-1} but this only applies when |r| > 1

    When |r| < 1, it's actually  S_n = \frac{a(1-r^n)}{1-r}

    I can show you proof of this if you like.
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