The equivalent resistance of the following infinite network of resistances is
AIIMS 1995, Medium
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$R = 2 + 2 + \frac{{2 \times R}}{{2 + R}}$ $ \Rightarrow $ $2R + {R^2} = 8 + 4R + 2R$
${R^2} - 4R - 8 = 0$ $ \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 $
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