Combining Capacitors

In parallel: the same voltage, the charges add:

$$\relax C = C_{1} + C_{2}$$

In series: the same charge, the voltages add:

$$\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}$$

A charged capacitor joined to an uncharged one shares its charge until both have the same voltage: $V = \frac{Q}{C_1 + C_2}$.