Infinite RC Circuit!

In the circuit shown, we have infinitely many resistors with resistance of R1=R,R2=R2,R3=R4, R_1 = R, R_2 = \frac{R}{2}, R_3 = \frac{R}{4} , \ldots. We also have infinitely many capacitors with capacitance of C1=C,C2=2C,C3=4C, C_1 = C, C_2 = 2C, C_3 = 4C ,\ldots . At t=0t=0 switch S is closed.

Find the ratio of potential drop (in volts) across capacitor Cn C_n and resistor RnR_n at time t=ReqCeqt=R_\text{eq}C_\text{eq}. Take e=2.718e=2.718.

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