An infinite ladder network of capacitors is constructed using identical capacitors, each of capacitance \(C\). As shown in the diagram, each stage consists of one capacitor in series along the top line, followed by one capacitor connected in parallel across the output line. Let \(C_N\) denote the equivalent capacitance across terminals \(A\) and \(B\) for a network truncated after \(N\) stages, and let \(C_{\text{eq}}\) denote the equivalent capacitance of the infinite network as \(N \to \infty\). Which choice correctly identifies the expression for \(C_{\text{eq}}\) and describes how \(C_N\) changes as the number of stages \(N\) increases?