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Math Help - Algebra help

  1. #1
    Junior Member
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    Jan 2007
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    Algebra help

    Could someone give me a hand with this one?

    Given that n[squared]+n=2k, how can (n+1)[squared]+(n+1) be written as a multiple of 2?

    Possible solutions:
    2(k+1)
    2(n+1)
    2(n+k)
    2(n+k+1)
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Quote Originally Posted by gretchen View Post
    Could someone give me a hand with this one?

    Given that n[squared]+n=2k, how can (n+1)[squared]+(n+1) be written as a multiple of 2?

    Possible solutions:
    2(k+1)
    2(n+1)
    2(n+k)
    2(n+k+1)
    Expand it and see from there.

    n^2 +n = 2k -----------(1)

    (n+1)^2 +(n+1)
    = (n^2 +2n +1) +(n+1)
    = n^2 +2n +1 +n +1
    = (n^2 +n) +2n +2
    = 2k +2n +2
    = 2(k +n +1) ----------------answer.
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