Capacitors In Series
Two capacitors are connected in series. In a series connection, the magnitude of charge on all plates is the same:
$$C_{1} V_{2} = Q = C_{2} V_{2}$$
$$\begin{aligned} V &= V_{1} + V_{2} \\ &= Q \left( \frac{1}{C_{1}} + \frac{1}{C_{2}} \right) \end{aligned}$$
The equivalent capacitance is:
$$\begin{aligned} \frac{1}{C_{eq}} &\equiv \frac{V}{Q} \\ &= \frac{1}{C_{1}} + \frac{1}{C_{2}} \end{aligned}$$
The reciprocal of the equivalent capacitance of a series combination equals the sum of the reciprocals of the individual capacitances.
Capacitors In Parallel
Two capacitors are connected in parallel. In a parallel connection, the potential difference for all individual capacitors is the same:
$$\frac{Q_{1}}{C_{1}} = V = \frac{Q_{2}}{V_{2}}$$
$$\begin{aligned} Q &= Q_{1} + Q_{2} \\ &= (C_{1} + C_{2}) V \end{aligned}$$
The equivalent capacitance:
$$\begin{aligned} C_{eq} &\equiv \frac{Q}{V} \\ &= C_{1} + C_{2} \end{aligned}$$
The equivalent capacitance of a parallel combination equals the sum of the individual capacitances.
Next: Energy Stored In Capacitors
