The general formalism relevant for studies of the contributions to the background of extragalactic sources is summarized. Analytic formulae, useful to highlight some basic aspects, are presented; many of them were, to our knowledge, never published before. In particular we point out and discuss the effect on source counts of a luminosity dependent K-correction, such as that appropriate for rich clusters of galaxies, and of a spectrum steeply increasing towards high frequencies as is the case for the sub-mm/mm spectrum of galaxies. Also we derive simple analytic approximations useful to compute the contribution of clustering to small scale fluctuations.
