Within about a year (1916-1917) Chapman and Enskog independently proposed an important expansion for solving the Boltzmann equation.However,the expansion is divergent or indeterminant in the case of relaxation time τ ≥ 1.Since then,this divergence problem has puzzled researchers for a century.Using a modified M(o)bius series inversion formula,we propose a modified Chapman-Enskog expansion with a variable upper limit of the summation.The new expansion can give not only a convergent summation but also the best-so-far explanation on some unbelievable scenarios occurring in previous practice.