The Parallel Resistance

The resistance of each resistor connected in the circuit is of 1Ω.

The equivalent resistance of the circuit = $R'$

$\large \therefore R' = 1 + \frac{R'}{R' + 1} + 1$

$\large \implies R'^2 - 2R' - 2 = 0$

$\large \implies R' = \frac{2 \pm \sqrt{4 + 8}}{2}$

$\large \implies R' = \frac{2 \pm \sqrt{12}}{2}$

$\large \implies R' = 1 \pm \sqrt{3}$

The negative value of resistance cannot be accepted. Hence $\large R' = 1 + \sqrt{3}$

$\large \therefore R' = 1 + \sqrt{3}$

$\large R' = 1 + 1.73205$ = $\large 2.73205\Omega$

$\therefore$ The Equivalent resistance of the infinite network is $\boxed {2.73205\Omega}$