+67 For \(0 \leq x \leq 1,\) the function \(f(x)\) satisfies the relations \(f\left(\dfrac x{x+1}\right) = \dfrac{f(x)}2\) and \(f(1-x) = 1 - f(x).\)
What is the value of the expression \(f\left(\dfrac23\right) + f\left(\dfrac25\right) + f\left(\dfrac27\right) + \dots + f\left(\dfrac2{2n+1}\right) + \dotsb\,? \)
Express your answer as a common fraction.
