  This paper establishes complete convergence for weighted sums and the
Marcinkiewicz--Zygmund-type strong law of large numbers for sequences of
negatively associated and identically distributed random variables
$\{X,X_n,n\ge1\}$ with general normalizing constants under a moment condition
that $ER(X)<\infty$, where $R(\cdot)$ 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, 1995) 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.
