Explanation

(c) Let the resultant resistance be $R.$ If we add one more branch, then the resultant resistance would be the same because this is an infinite sequence
$\therefore\frac{RR_{2}}{R + R_{2}} + R_{1} = R \Rightarrow 2R + R + 2 = R^{2} + 2R$
$\Rightarrow R^{2} - R - 2 = 0 \Rightarrow R = - 1$ or $R = 2ohm$
$R = 2 + 2 + \frac{2 \times R}{2 + R} \Rightarrow 2R + R^{2} = 8 + 4R + 2R$
$\Rightarrow R^{2} - 4R - 8 = 0 \Rightarrow R = \frac{4 \pm \sqrt{16 + 32}}{2} = 2 \pm 2\sqrt{3}$
$R$ cannot be negative, hence $R = 2 + 2\sqrt{3} = 5.46\Omega$