Convergence properties of symmetry-adapted perturbation expansions for nonadditive interactions are tested by performing high-order calculations for three spin-aligned hydrogen atoms. It is shown that the strong symmetry forcing characteristic of the Hirschfelder-Silbey theory leads to a rapidly convergent perturbation series. The symmetrized Rayleigh-Schrodinger perturbation theory employing a weak symmetry forcing is shown to provide in low orders accurate approximations to the nonadditive part of the interaction energy. In very high orders the convergence of this perturbation expansion becomes very slow, and the series converges to an unphysical limit, very close to the exact interaction energy. The nonadditive part of the interaction energy for the lowest quartet state of H-3 is interpreted in terms of the first-order exchange, induction, exchange-induction, exchange-dispersion, induction-dispersion, and dispersion contributions. It is shown that even for such a simple trimer the correct description of these components is necessary to obtain quantitative agreement with variational full configuration interaction results.