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Let{Xn,n≥1}be a sequence of α-stable random variables(0<α<2),{αni,1≤i≤n,n≥1}be an array of constant real numbers .Under some restriction of {αni,1≤i≤n,n≥1},the authors discuss the integral test for the weighted partial sums {∑i=1^nαniXi,n≥1},and obt