Question

derive an expression for the total capacitance when three capacitors are joined in series.

Answer 1

Let the three capacitors connected in series be C1, C2, and C3

Also Let the Current flowing through these capacitors be Q'
Let V1 be the Voltage Across C1
V2 be the voltage across C2
V3 be the voltage across C3

Since      V = Q / C

Thus
V' = Q/ C = Q'/ C1 + Q'/ C2 + Q'/ C3
      Thus 

Clearly
              1/ C = 1/ C1 + 1/ C2 + 1/ C3
this is the total capacitance in series