For an infinite ladder network, adding one more repeating unit to the chain does not change the total equivalent resistance ($R_{eq}$). Assuming the network consists of repeating units with a series resistor $R_1 = 2\ \Omega$ and a parallel resistor $R_2 = 1\ \Omega$ (which yields the given answer), the equivalent resistance satisfies the equation: $R_{eq} = R_1 + \frac{R_{eq}R_2}{R_{eq} + R_2}$. Substituting values: $R_{eq} = 2 + \frac{R_{eq}(1)}{R_{eq} + 1}$. Rearranging gives the quadratic equation: $R_{eq}^2 - 2R_{eq} - 2 = 0$. Solving for $R_{eq}$ using the quadratic formula: $R_{eq} = \frac{2 \pm \sqrt{4 - 4(1)(-2)}}{2} = \frac{2 \pm \sqrt{12}}{2} = 1 \pm \sqrt{3}$. Since resistance cannot be negative, $R_{eq} = (1 + \sqrt{3})\ \Omega$.