The ratio $R_{1}/R_{2}$ is

Here, Voltage in every point is increasing proportionally.

Given ,

$V_1 =\dfrac {V_0}{k}, V_2 =\dfrac {V_1}{k}, V_3 =\dfrac {V_2}{k},$

$\ I=I_1 +I_2$

$\dfrac {V_0-V_0 /k}{R_1}=\dfrac {V_0/ k-V_0 /k^2}{R_1}+\dfrac {V_0 /k}{R_2}$

$\dfrac {R_1}{R_2}=\dfrac {(k-1)^2}{k}$