Why we use capacitors in ceiling fen?

My thought about it is that it's used as a smoothing capacitor so as to produce a d.c. from the a.c.

Though I would think that with modern means, a system of solenoids can be used to act as a motor using the provided a.c. instead of using a d.c. to run a motor.

We cannot convert ac to dc by using capacitors.we use capacitors in fan because it contains single phase induction motor which does not produce rotating magnetic field.In order to produce this kind of field we split the phase with the help of capacitor .