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Math Help - Closed Formula for Geometric Series and Sums

  1. #1
    Junior Member
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    Closed Formula for Geometric Series and Sums

    I just have two questions regarding closed form formulas for geometric series and summing infinite series.

    For the closed form formula, I have an expression for the nth term:

    7(7/8)^n

    But I am not sure how to convert this to closed form since I am not really sure what closed form looks like. Is it just to convert it into a finite sum equation like this:

    <br />
\frac{7(1-\frac {7} {8}^n)} {(1- \frac {7} {8})}

    For the infinite series, I have the formula:

    \frac {1} {4} \sqrt{h}

    Where h = 7(7/8)^n

    So the very first term would be:

    \frac {1} {4} \sqrt{7\frac {7} {8}}

    And this would go in the numerator, but I am not sure what would go in the denominator. I really appreciate everyone's help.
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    1,092
    Quote Originally Posted by Spudwad View Post
    I just have two questions regarding closed form formulas for geometric series and summing infinite series.

    For the closed form formula, I have an expression for the nth term:

    7(7/8)^n

    But I am not sure how to convert this to closed form since I am not really sure what closed form looks like. Is it just to convert it into a finite sum equation like this:

    <br />
\frac{7(1-\frac {7} {8}^n)} {(1- \frac {7} {8})}
    This is almost perfect, but remember, the first term of that series is not 7. it is 7 \cdot \frac{7}{8}.

    For the infinite series, I have the formula:

    \frac {1} {4} \sqrt{h}

    Where h = 7(7/8)^n

    So the very first term would be:

    \frac {1} {4} \sqrt{7\frac {7} {8}}

    And this would go in the numerator, but I am not sure what would go in the denominator. I really appreciate everyone's help.
    What's the common ratio? You're taking the square root of \left(\frac{7}{8}\right)^n, which is \left(\frac{7}{8}\right)^{0.5 \cdot n} = \left(\left(\frac{7}{8}\right)^{0.5}\right)^n.
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