Truncation of Schwinger-Dyson equations and the 1/N expansion in the O(N) model

We use the O({ital N}) model as a nonperturbative example to study the effect of truncating the Schwinger-Dyson sequence of equations. We show that truncation of this hierarchy leads in the O({ital N}) model to solutions for the propagators and vertex functions correct to a definite power of 1/{ital N}. The procedure can be used to generate a systematic expansion in 1/{ital N} for an arbitrary Green's function of the model.