The entropy of 1-1 and 2-2 model electrolytes is calculated from an expansion in terms of the multiparticle correlation functions; For electrolytes, a simple truncation of this expansion is never sufficient for the accurate calculation of the entropy, even in the limit of low concentration, in marked contrast to the behavior for short-ranged potentials. However, a partial, but infinite-order, summation of the expansion is shown to yield both the correct low-concentration limit and excellent results over a wide range of concentrations for both 1-1 and 2-2 electrolytes. The consequences of this result for some earlier applications of the entropy expansion to electrolytes are discussed.