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We use the virial expansion to investigate the behavior of the two-component,attractive Fermi gas in the high-temperature limit, where the system smoothlyevolves from weakly attractive fermions to weakly repulsive bosonic dimers asthe short-range attraction is increased. We present a new formalism forcomputing the virial coefficients that employs a diagrammatic approach to thegrand potential and allows one to easily include an effective range $R^*$ inthe interaction. In the limit where the thermal wavelength $\lambda \ll R^*$,the calculation of the virial coefficients is perturbative even at unitarityand the system resembles a weakly interacting Bose-Fermi mixture for allscattering lengths $a$. By interpolating from the perturbative limits$\lambda/|a| \gg 1$ and $R^*/\lambda \gg 1$, we estimate the value of thefourth virial coefficient at unitarity for $R^*=0$ and we find that it is closeto the value obtained in recent experiments. We also derive the equations ofstate for the pressure, density and entropy, as well as the spectral functionat high temperatures.

High-temperature limit of the resonant Fermi gas