An infinite sequence of resistance is shown in the figure. The resultant resistance between A and B, when R₁ = 1 ohm and R₂ = 2 ohm, will be

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.

$\begin{array}{l}\therefore \frac{{\mathrm{RR}}_2}{\mathrm{R}+{\mathrm{R}}_2}+{\mathrm{R}}_1=\mathrm{R}\Rightarrow 2\mathrm{R}+\mathrm{R}+2={\mathrm{R}}^2+2\mathrm{R}\\ \Rightarrow {\mathrm{R}}^2-\mathrm{R}-2=0\Rightarrow \mathrm{R}=-1\mathrm{\Omega }\mathrm{or}2\mathrm{\Omega }\end{array}$

Since $-1\Omega$ does not have any sense, so neglecting it.