The concept of truth degrees of formulas in (L)ukasiewicz n-valued proposi tional logic Ln is proposed. A limit theorem is obtained, which says that the truth function (T)n induced by truth degrees converges to the integrated truth function (T) when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued (L)ukasiewicz logic and the continuous valued (L)ukasiewicz logic. Moreover, the results obrained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.