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Math Help - Contest problem 2

  1. #1
    Junior Member Kanwar245's Avatar
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    Contest problem 2

    What is the value of the expression: 1-2-3+4-5+6-7+8-.....-2011+2012?
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  2. #2
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    Re: Contest problem 2

    Quote Originally Posted by Kanwar245 View Post
    What is the value of the expression: 1-2-3+4-5+6-7+8-.....-2011+2012?
    1-2-3+4 = 0
    -5 + 6 = 1
    -7 + 8 = 1 ....continue

    OK?
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  3. #3
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    Re: Contest problem 2

    Quote Originally Posted by Kanwar245 View Post
    What is the value of the expression: 1-2-3+4-5+6-7+8-.....-2011+2012?
    I think that you have some sign errors in the statement of the question.

    \sum\limits_{k = 1}^N {\left( {2k - 1} \right)}  = N(N + 1) - N = {N^2}

    \sum\limits_{k = 1}^N {\left( {2k } \right)}  = N(N + 1) = {N^2+N}
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    Re: Contest problem 2

    If no sign errors: (2012-4) / 2 - 1004

    If -1+2-3+4-5+6....: 2012 / 2 = 1006 (net of 1 per pairs)
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  5. #5
    Junior Member Kanwar245's Avatar
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    Re: Contest problem 2

    No there are no sign errors, so ans is 1004
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