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Math Help - closed form sequence

  1. #1
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    closed form sequence

    The problem: Find a closed form of the following sequence 0,3,2,5,4,7,6,9,8,11,10,13,12.

    So I get that the odds are n-1 and the evens are n+1 and I've started the equation and so far I have ((-1)^(n-1) + 1)/2 + ((-1)^n + 1)/2) (the first part is supposed to be (-1)^(n-1)) the first half to find the odd numbers and the second to find the even numbers.

    I'm having trouble coming up with where to put the n-1 and n+1. Any help or hints is appreciated.

    Thanks.
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  2. #2
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    nevermind.... im dumb.

    thanks anyways.
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  3. #3
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    Hello, geoffl!

    You're not dumb . . . If you are, you've got company.


    Find a closed form for the sequence: 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12.

    I too got distracted by the odd/even subsequences

    . . and got involved with \frac{1-(\text{-}1)^n}{2} and \frac{1 + (\text{-}1)^n}{2} . (the "blinker functions")


    It took me a while to see a simpler explanation.

    . . If n is odd, subtract 1 from n.
    . . If n is even, add 1 to n.

    Therefore: . f(n) \;=\;n + (\text{-}1)^n

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