An infinite sequence of resistance is shown in the figure. The resultant resistance between $A$ and $B$ will be, when ${R_1} = 1\,ohm$ and ${R_2} = 2\,ohm$ ............. $\Omega$
Medium
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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.
$\therefore \frac{{R{R_2}}}{{R + {R_2}}} + {R_1} = R \Rightarrow 2R + R + 2 = {R^2} + 2R$
$ \Rightarrow {R^2} - R - 2 = 0 \Rightarrow R = - 1$ or $R = 2\,ohm$
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