  This paper demonstrates that a computer aided perturbation theory can easily
be realized by use of a cumulant approach. In contrast to a recent alternative
formulation on the basis of Wegner's flow equation method the present approach
can be applied to systems with arbitrary Hilbert space. In particular an
equidistant spectrum of the unperturbed part of the Hamiltonian is not needed.
The method is illustrated in detail for dimerized and frustrated spin 1/2
chains for which the ground state energy is calculated up to seventh order
perturbation theory.
