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Math Help - sum of multiples

  1. #1
    Junior Member Bartimaeus's Avatar
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    sum of multiples

    I just can't see it at the moment.


    Find the sum of all positive integers less than 10,000 not divisible by seven.


    Thanks guys.
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  2. #2
    MHF Contributor red_dog's Avatar
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    From the sum of all positive integers less than 10000, substract the sum of all positive integers which are divisible by 7.
    \displaystyle\sum_{k=1}^{10000}k-\sum_{k=1}^{1428}7k
    and use \displaystyle\sum_{k=1}^nk=\frac{n(n+1)}{2}
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