Let the equivalent resistance be $x$. Removing one repeated section, the rest of the network (x) is in parallel with the 1 $\Omega$ rung, in series with the two 1 $\Omega$ resistors: $\frac{x\times1}{x+1}+2=x \Rightarrow x^2-2x-2=0 \Rightarrow x=\frac{2\pm2\sqrt{3}}{2}=1\pm\sqrt{3}$. Neglecting the negative value, $x=(1+\sqrt{3})\ \Omega$.