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Math Help - Summation of summation?

  1. #1
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    Sep 2008
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    Summation of summation?

    I want to figure out the proper summation to figure out a sum of products:
    5
    x3
    ----
    15
    x3
    ----
    45
    x3
    ----
    135
    x3
    ___
    ...

    So if n=0 the result is 5, if n=1 the result is 5+15, if n=2, the result is 5+15+45 and so. Hopefully that makes sense. I'm not quite sure how else to put it. Would the best way be to do something like \sum_{i=0}^{n}5\sum_{j=0}^{i}3^j? Or is there some more concise way of putting it? I appreciate any help you guys can offer. Thanks.
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  2. #2
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    Quote Originally Posted by blcArmadillo View Post
    I want to figure out the proper summation to figure out a sum of products:
    5
    x3
    ----
    15
    x3
    ----
    45
    x3
    ----
    135
    x3
    ___
    ...

    So if n=0 the result is 5, if n=1 the result is 5+15, if n=2, the result is 5+15+45 and so. Hopefully that makes sense. I'm not quite sure how else to put it. Would the best way be to do something like \sum_{i=0}^{n}5\sum_{j=0}^{i}3^j? Or is there some more concise way of putting it? I appreciate any help you guys can offer. Thanks.
    Try

    \displaystyle 5\sum_{i=0}^n3^i
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