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?
Work backwards.
$\displaystyle f(2007)\ =\ f(2(1003)+1)$
$\displaystyle =\ f(1003)$
$\displaystyle =\ f(2(501)+1)$
$\displaystyle =\ f(501)$
$\displaystyle =\ f(2(250)+1)$
$\displaystyle =\ f(250)$
$\displaystyle =\ f(2(125))$
$\displaystyle =\ 1-f(125)$
$\displaystyle \vdots$
etc.