We compute the abelianization of the Jennings group Jk(Z) of powers series with constant coefficient 0, linear coefficient equal to 1 and vanishing coefficients in orders greater or equal than 2 and less than k, where k >= 2. This is accomplished by directly dealing with the equivalence classes in the corresponding abelianizations, in contrast with the work of I. K. Babenko and S. A. Bogaty, who in 2008 gave an explicit abelianization morphism for the case k=2.