Here, a new approach to derive expressions for the probability of error PEin the binary detection problem is studied. It is demonstrated that series expressions for PEand the consequent tight yet simple bound on PEare frequently readily derived and; in many cases, have advantages over the more familiar analytical closed form expressions for PE. A major advantage is the applicability of the series approach to certain communication systems where the probability density function of the sufficient statistic cannot be derived in convenient analytical form but the characteristic function of the sufficient statistic is available. The attractive features of the series approach, e.g., simplicity of derivation, reduced computational effort, and tight error bounds, are first established for some classic systems and then are investigated for some communication systems of practical interest for Which no expression for the probability of error exists in the present literature. The research reported here arose from a need to study the Rician and Rayleigh fading diversity channels and results for these channels are given in some detail.