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Math Help - expression to result in -1 or 1

  1. #1
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    expression to result in -1 or 1

    Is there an expression that results in -1 or 1 for these values of n:
    1 -> -1
    2 -> -1
    3 -> 1
    4 -> 1
    5 -> -1
    6 -> -1
    7 -> 1
    8 -> 1
    9 -> -1
    10 -> -1
    etc.
    My book has something that does not work correctly.
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  2. #2
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    Re: expression to result in -1 or 1

    Quote Originally Posted by Stuck Man View Post
    Is there an expression that results in -1 or 1 for these values of n:
    1 -> -1
    2 -> -1
    3 -> 1
    4 -> 1
    5 -> -1
    6 -> -1
    7 -> 1
    8 -> 1
    9 -> -1
    10 -> -1
    etc.
    My book has something that does not work correctly.
    a_n  = \left( { - 1} \right)^{\left\lfloor {\frac{{n + 1}}{2}} \right\rfloor } where \left\lfloor {\frac{{n + 1}}{2}} \right\rfloor is the floor function (greatest integer function).
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  3. #3
    MHF Contributor chisigma's Avatar
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    Re: expression to result in -1 or 1

    Quote Originally Posted by Stuck Man View Post
    Is there an expression that results in -1 or 1 for these values of n:
    1 -> -1
    2 -> -1
    3 -> 1
    4 -> 1
    5 -> -1
    6 -> -1
    7 -> 1
    8 -> 1
    9 -> -1
    10 -> -1
    etc.
    My book has something that does not work correctly.
    I am 'enthusiast' of circular functions so that I propose...

    a_{n}= \sqrt{2}\ \sin (1-2n)\ \frac{\pi}{4} (1)

    Kind regards

    \chi \sigma
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  4. #4
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    Re: expression to result in -1 or 1

    Is that often featured on calculators? I don't think I've seen it before although I've heard of it in computer languages.
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  5. #5
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    Re: expression to result in -1 or 1

    Quote Originally Posted by Stuck Man View Post
    Is that often featured on calculators? I don't think I've seen it before although I've heard of it in computer languages.
    I know nothing about calculators, but on a CAS it is floor(x).
    Look at this webpage.
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