The equivalent resistance between points A and B of an infinite network of resistances, each of 1Ω, connected as shown, is:
Answer & explanation
Correct answer: option 3
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 $x^2-x-1=0$
$x=\frac{1+\sqrt{1+4}}{2}=\frac{1+\sqrt{5}}{2} \Omega$