Use the Gibbs-Duhem equation to show that, if the activity coefficients of the components of a binary solution can be expressed as ln gamma_A = alpha_1 X_B + 1/2 alpha_2 X^2_B + 1/3 alpha_3 X^3_B + ... and ln gamma_B = beta_1 X_A + 1/2 beta_2 X^2_A + 1/3 beta_3 X^3_A + ... over the entire range of composition, then alpha_1 = beta_1 = 0, and that, if the