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Math Help - Geometric Series

  1. #1
    Member SengNee's Avatar
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    Pangkor Island, Perak, Malaysia.
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    Geometric Series

    Find the number of terms and the sum of the geometric series below.

    x+x^3+x^5+...+x^25

    Answer:
    n=13
    S_{13}=\frac{x(1-x^{26})}{1-x^2}

    Why the answer given is
    S_{13}=\frac{x(1-x^{26})}{1-x^2}
    but not
    S_{13}=\frac{x(x^{26}-1)}{x^2-1}
    ?
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by SengNee View Post
    Find the number of terms and the sum of the geometric series below.

    x+x^3+x^5+...+x^25

    Answer:
    n=13
    S_{13}=\frac{x(1-x^{26})}{1-x^2}

    Why the answer given is
    S_{13}=\frac{x(1-x^{26})}{1-x^2}
    but not
    S_{13}=\frac{x(x^{26}-1)}{x^2-1}
    ?
    As far as I can remember(and I did series a long time ago), it does not matter how they are arranged. You should arrive at the same answer I think(EDIT: Yes you will).

    If r < 1 then we use one of the arrangements, and if r > 1 then we use the other. (EDIT: Only to make things easier)
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  3. #3
    Super Member wingless's Avatar
    Joined
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    Istanbul
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    Quote Originally Posted by SengNee View Post
    Why the answer given is
    S_{13}=\frac{x(1-x^{26})}{1-x^2}
    but not
    S_{13}=\frac{x(x^{26}-1)}{x^2-1}
    ?
    What's the difference? Multiply both the numerator and denominator by -1 and you get the same thing..
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