With series connected resistors, the sum of all the voltage drops across the series circuit will be equal to the applied voltage VS ( Kirchhoff’s Voltage Law ) and this is also true about capacitors in series. With series connected capacitors, the capacitive reactance of the capacitor acts as an impedance due to the frequency of the supply.
The capacitance doesn't increase in series; it decreases. Capacitors in parallel are capacitors that are connected with the two electrodes in a common plane, meaning that the positive electrodes of the capacitors are all connected together and the negative electrodes of the capacitors are connected together.
Combining capacitors in series reduces the total capacitance, and isn't very common, but what are some possible uses for it? It shouldn't be used to increase the voltage rating, for instance, since you can't guarantee that the middle will be at half the DC voltage of the total, without using bleeder resistors.
Connecting them in series increases the voltage capability (add voltage limits of all caps in series). To have robustness against short circuit specially ceramic capacitors that are connected to power lines. If capacitor shorts, it can burnt PCB trace or worst it may cause fire.
However, when the series capacitor values are different, the larger value capacitor will charge itself to a lower voltage and the smaller value capacitor to a higher voltage, and in our second example above this was shown to be 3.84 and 8.16 volts respectively.
However, it is far better to get a single capacitor that meets the higher voltage threshold on its own as combining capacitors in series will also lead to a higher Effective Series Resistance (ESR). In the scenario above, you will double the ESR. High ESR can cause unwanted or catastrophic effects on circuits not designed to handle it.