  A strictly truncated (weak-coupling) perturbation theory is applied to the
attractive Holstein and Hubbard models in infinite dimensions. These results
are qualified by comparison with essentially exact Monte Carlo results. The
second order iterated perturbation theory is shown to be quite accurate in
calculating transition temperatures for retarded interactions, but is not as
accurate for the self energy or the irreducible vertex functions themselves.
Iterated perturbation theory is carried out thru fourth order for the Hubbard
model. The self energy is quite accurately reproduced by the theory, but the
vertex functions are not. Anomalous behavior occurs near half filling because
the iterated perturbation theory is not a conserving approximation. (REPLACED
WITH UUENCODED FIGURES AT THE END. THE TEXT IS UNCHANGED)
