The equivalent resistance between points A and B of an infinite network of resistances, each of 1Ω, connected as shown, is:

infinite 2Ω $\frac{1+\sqrt{5}}{2}$ Ω zero

$\frac{1+\sqrt{5}}{2}$ Ω

Let RAB = x. Then, $R_{AB}=1+\frac{x}{1+x}$        or        $x=1+\frac{x}{1+x}$ ∴  $x+x^2=1+x+x$        or        $x^2-x-1=0$ $x=\frac{1+\sqrt{1+4}}{2}=\frac{1+\sqrt{5}}{2} \Omega$