Series connection or serial connection is a way of connecting elements in an electrical circuit where the same current flows through all elements, and thus, the current is the same in all elements.
For elements connected in series (1, 2, ... n), the current passing through them is the same:
$$I=I_{1}=I_{2}=...=I_{n}$$
The sum of voltages across the elements in the circuit is equal to the supply voltage:
$$U=U_{1}+U_{2}+...+U_{n}$$
The total resistance of the series circuit is equal to the sum of the resistances of the individual elements:
$$R=R_{1}+R_{2}+...+R_{n}$$