For a series connection of capacitors the current that flows through them is the same, therefore the charge in each of them is the same. Though the sum of voltages across each capacitor must equal to source voltage. That is:

Q=CeqV or V=Q/Ceq

V1=Q/C1, V2=Q/C2, V3=Q/C3.

But V=V1+V2+V3

Substitute into this last equation and solve for Ceq.

For a series connection of capacitors the current that flows through them is the same, therefore the charge in each of them is the same. Though the sum of voltages across each capacitor must equal to source voltage. That is:

\$Q=C_{eq}V\$ or \$V=\frac{Q}{C_{eq}}\$

\$V_1=\frac{Q}{C_1},V_2=\frac{Q}{C_2} ,V_3=\frac{Q}{C_3} \$.

But \$V=V_1+V_2+V_3\$

Substitute into this last equation and solve for \$C_{eq}\$.