Utilizing the grand canonical partition function as well as the cumula
nt summation formula, we consider a systematic approximation scheme fo
r a strongly correlated fermion system. As an example, we investigate
the single-impurity Anderson model. We are motivated by the fact that
for this model there are physical aspects to the approximations used t
hat are simply understood. In particular the lowest-order truncation y
ields the Kondo temperature as well as a many-particle understanding o
f the approximation of Zwicknagl, Zevin, and Fulde to the f spectral f
unction.