This paper establishes complete convergence for weighted sums and the Marcinkiewicz-Zygmundtype strong law of large numbers for sequences of negatively associated and identically distributed random variables {X, X n , n ≥ 1} with general normalizing constants under a moment condition that ER(X) < ∞, where R(•) is a regularly varying function. The result is new even when the random variables are independent and identically distributed (i.i.d.), and a special case of this result comes close to a solution to an open question raised by Chen and Sung (Statist Probab Lett 92:45-52, 2014). The proof exploits some properties of slowly varying functions and the de Bruijin conjugates. A counterpart of the main result obtained by Martikainen (J Math Sci 75(5):1944-1946 on the Marcinkiewicz-Zygmund-type strong law of large numbers for pairwise i.i.d. random variables is also presented. Two illustrated examples are provided, including a strong law of large numbers for pairwise negatively dependent random variables which have the same distribution as the random variable appearing in the St. Petersburg game.

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