A typical capacitor connection in series will look like the one I draw below:
“In series” is literally saying that the capacitors are wired "serially", one after another (no seperate branches), When a potential difference V is applied across several capacitors in series connection, the capacitors have identical charge q. The sum of the potential differences across all the capacitors (in this case C1,C2&C3) is equal to the applied potential difference V across the two ends of series connetion, in this case the left side of C1 and right side of C3.
Therefore we can express these properties in formula as : V1 = q/C1, V2 = q/C2, V3 = q/C3, Vtotal = V1+V2+V3= q (1/C1 + 1/C2 + 1/C3)
If we are looking for Ctotal, then that's equal to Ctotal=q/Vtotal=q/ [q (1/C1 + 1/C2 + 1/C3)]=1/ (1/C1 + 1/C2 + 1/C3)
Normally we use the formula in this format: 1/Ctotal = 1/C1 + 1/C2 + 1/C3
Capacitors that are connected in series can be regarded as a capacitor that has the same charge q and V (total) as the actual series capacitors.
So, if there are n capacitors connected in series connection, then we can say: 1/Ctotal=`sum_(i=1)^n ``1/(Ci)`
Hope this is helpful for your studies!