2. Electric potential and capacitance — Physics STD 12 Science — Question

So we can remove all of these

For one series

$\frac{1}{C_{e q}}=\frac{1}{C}+\frac{1}{2 C}+\frac{1}{4 C}+\frac{1}{8 C}+\ldots$

$=\frac{1}{C}\left(1+\frac{1}{2}+\frac{1}{4}+\ldots .\right)$

$=\frac{1}{C} \times \frac{1}{1-\frac{1}{2}}=\frac{2}{C}=\left(S_{\infty}=\frac{1}{1-r}\right)$

$\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{\mathrm{C}}{2}$