Capacitance combines the other way round from resistance. Capacitors in parallel share the same voltage and their plate areas effectively add, so the capacitances add. In series the charge has to pass through every capacitor in turn, so the reciprocals add and the total is smaller than the smallest part.
Why you would put capacitors in series
Almost always for voltage rating rather than for capacitance. Two 400 V capacitors in series withstand 800 V but give you half the capacitance. In practice you also need balancing resistors across each one, because leakage currents differ and the voltage will not divide evenly on its own.
Energy and charge
A charged capacitor holds Q = CV coulombs and stores E = ½CV² joules. The square matters: doubling the voltage quadruples the stored energy. A 470 µF capacitor at 400 V holds about 38 J, which is enough to be dangerous long after the power is off. Discharge large capacitors through a resistor before touching a board.
Real capacitors are not ideal
Ceramic capacitors lose a large fraction of their nominal value under DC bias — a 10 µF X5R part can fall below 3 µF at its rated voltage. Electrolytics have tolerances as wide as −20/+80% and series resistance that matters in switching supplies. Use the calculated figure as a design target, not a guarantee.