Let us connect n number of capacitors in series. V volt is applied across this series combination of capacitors.
Let us consider capacitance of capacitors are C_{1},C_{2}, C_{3}…….C_{n} respectively, and equivalent capacitance of series combination of the capacitors is C. The voltage drops across capacitors are considered to be V_{1}, V_{2}, V_{3}…….V_{n}, respectively.

Now, if Q coulomb be the charge transferred from the source through these capacitors, then,
Since, the charge accumulated in each capacitor and I entire series combination of capacitors will be same and it is considered as Q.
Now, equation (i) can be written as,

Capacitors in Parallel

Let us connect n number of capacitors in parallel, across a voltage source of V volt.
Let us consider the capacitance of the capacitors are C_{1}, C_{2}, C_{3}…..C_{n}, respectively and equivalent capacitance of the combination of the capacitor is C.
As the capacitors are connected in parallel, like current charge in each capacitor will be same. Total charge of the parallel combination, will be divided in each capacitor according to it’s capacitance value but voltage across each capacitor will be same and at steady state condition it is exactly equal to the applied voltage.
Where,Q_{1}, Q_{2}, Q_{3},…….Q_{n} are the charge of capacitor C_{1}, C_{2}, C_{3}….. C_{n} respectively.
Now equation (2) can be written as,
Therefore equivalent capacitance of series connected capacitors is reciprocal of sum of reciprocal of capacitance of each capacitor.
Equivalent capacitance of parallel connected capacitors is sum of capacitance of each capacitor.