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Math Help - functions n

  1. #1
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    functions n

    let 'f' be a function defined on non-negative integers satisfying the following conditions: f(2n+1) = f( n ) & f(2n) = 1 - f( n )
    find f(2007.

    need a little bit of help here.. how do i start?
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Work backwards.

    f(2007)\ =\ f(2(1003)+1)

    =\ f(1003)

    =\ f(2(501)+1)

    =\ f(501)

    =\ f(2(250)+1)

    =\ f(250)

    =\ f(2(125))

    =\ 1-f(125)

    \vdots

    etc.
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  3. #3
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    i got all the way till f(1)... then?
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  4. #4
    Senior Member TheAbstractionist's Avatar
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    Thatís it. The answer is f(1) (which should be given to you).

    In order to define the series, the first two values, namely f(0) and f(1), must be given.
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