Let ∑ cj and ∑dj be, respectively, convergent and divergent series of positive terms and let ∑ aj be a third series of positive terms. It is well known, [1, pg. 275] that ∑ aj converges if lim sup(aj/cj)<+∞, but diverges if liminf(aj/dj)>0. In this note we prove a generalized version of this comparison test that relies not on term-by-term comparison of the series, but on the relative densities of the terms of the series.