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Math Help - Log problem.

  1. #1
    Senior Member
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    Feb 2008
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    383

    Log problem.

    \frac{1}{n}-\frac{-1^n}{n^2}<0.000001

    can i solve this algebraically?
    if not, how do i solve it?

    many thanks.
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  2. #2
    MHF Contributor Amer's Avatar
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    May 2009
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    Jordan
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    1,093

    Re: Log problem.

     \frac{n - (-1)^n}{n^2} < \frac{1}{1000000}

    take n even 2k instead of n

     \frac{2k - 1}{4k^2} < \frac{1}{1000000}

    can you solve it ??

    try n odd sub 2k+1 instead of n
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  3. #3
    Senior Member
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    Feb 2008
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    Re: Log problem.

    for even, k>499999
    for odd, k>500000

    how to i proceed?

    how answer should be 1000002.

    i can see if i add the two ks, it comes to k>1000001

    is this the way to do it?

    many thanks.
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  4. #4
    Super Member Quacky's Avatar
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    Nov 2009
    From
    Windsor, South-East England
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    901

    Re: Log problem.

    for even, k>499999 So \frac{n}{2}>499999 remembering that n=2k

    for odd, k>500000 So \frac{n-1}{2}>500000 remembering that n=2k+1

    What is the solution which satisfies for all n?
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