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Math Help - tricky!

  1. #1
    Member
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    Sep 2009
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    106

    Smile tricky!

    help,,, the geom is tricky

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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Dec 2008
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    South Coast of England
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    Hello aeroflix

    Here's the solution to number 1.

    Suppose we take n natural numbers starting from m. Then their sum is:
    S = \tfrac{1}{2}n(2m+n-1)
    =1000
    \Rightarrow n(2m+n-1) = 2000

    \Rightarrow m = \frac12\left(\frac{2000}{n}-n+1\right)
    \Rightarrow n is a factor of 2000 and \frac12\left(\frac{2000}{n}-n+1\right) is a natural number.

    You'll find that this is satisfied for:
    n=1, m = 1000

    n=5,m=198

    n=16,m=55

    n=25,m=28
    I'll leave you to write down the resulting sequences of numbers.

    Grandad
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