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In this work, suppose that { Xn   ;  n  ≥ 1}is a sequence of asymptotically negatively associated random variables and { ani   ; 1 ≤  i  ≤  n ,  n  ≥ 1} is an array of real numbers such that∑   i  =  1   n|    a   n  i|    q=  O   (  n  )for some  q  &gt; max{α  p  −  1    α  −  1  /  2    ,  2   }with  αp  &gt; 1 andα  &gt;   1  2. Let  l  ( x ) &gt; 0 be a slowly varying function at infinity. We establish some equivalent conditions of the complete convergence for weighted sums of this form

Limit Theorems for Weighted Sums of Asymptotically Negatively Associated Random Variables Under Some General Conditions