Description: Actuarial literature in the twenty-five years includes discussions of a well known inequality. Among the recent papers on various aspects of this classic result are those by Berin 1970, Olson 1975 and Sarason 1960. A standard method for achieving this inequality uses Jensen's inequality. This is the method used by Bowers, et al 1983. We will also employ this method in an attempt to learn about it.