A method is presented here to sum certain type of Fourier series. The series is treated as a response function of a linear electric circuit with lumped constants. This electric circuit, subjected to the action of an external force expressed in the form of another Fourier series derived from the original series to be summed can be formed by inspection or by network synthesis. If this derived series can be put into a closed form, then by applying the steady-state operational technique to this electric circuit, the original series can be expressed in a closed form or in a graphical form.