[en] A power-series method for solving the kinetic equation is proposed. A simple procedure for deriving equations for arbitrary moments of the distribution function is described. An analysis of wave propagation in a stationary uniform hot magnetoactive plasma shows that allowance for tensors of ranks up to n and omission of higher rank tensors in the equations of tensor magnetohydrodynamics corresponds to taking into account waves at cyclotron harmonics with numbers up to n inclusive and ignoring higher harmonics. Thus, from the standpoint of accuracy and complexity of plasma description, tensor magnetohydrodynamics occupies an intermediate position between the kinetic approach and the conventional magnetohydrodynamics with a scalar pressure.