Let ｛X/sun ni/ ｜ 1 ≤ i ≤ n, n ≥ 1 ｝ be an array of rowwise negatively associated random variables. We in this paper discuss the conditions of n^-1p/ (equation omitted) →0 completely as n → ∞ for some 1 ≤ p < 2 under not necessarily identically distributed setting. As application, it is obtained that n^-1p/ (equation omitted) →0 completely as n → ∞ if and only if E｜X₁₁｜^2p < ∞ and EX/sub ni=0 under identically distributed case such that the corresponding results on i. i. d. case are extended and the strong convergence for weighted sums of rowwise negatively associated arrays is also considered.