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A network of resistance is constructed with \( R_{1} \) and \( R_{2} \) as shown in the figure. The potential at the points \( 1,2,3, \ldots \ldots . ., N \) are \( V_{1}, V_{2}, V_{3}, \ldots \ldots \ldots ., V_{n} \) respectively each having a potential \( K \) time smaller than previous one. Find:
\( \left(\frac{R_{1}}{R_{2}}\right) \times\left(\frac{R_{2}}{R_{3}}\right) \) in terms of \( \mathrm{K} \).
(A) \( \mathrm{K}-1 \)
(B) \( \mathrm{K}^{2}-1 \)
(C) \( \frac{1}{\mathrm{~K}+1} \)
(D) \( \frac{\mathrm{K}-1}{\mathrm{~K}+1} \)
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