Question #88844

An infinite ladder network of capacitors is constructed across two main terminals, $A$ and $B$. The network is composed of identical repeating unit cells. Each unit cell consists of a shunt capacitor $C_1$ connected directly across the input terminals of that cell, and a series capacitor $C_2$ connecting the upper input terminal to the upper input terminal of the subsequent cell. The lower terminals of all cells are connected to a common ideal wire. Given $C_1 = C$ and $C_2 = \Delta C$, where $C$ and $\Delta C$ are in Farads ($\text{F}$) and $\Delta C \ll C$. Which of the following expressions correctly represents the equivalent capacitance $C_{AB}$ across the terminals $A$ and $B$, approximated to the second order in $\frac{\Delta C}{C}$?