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Let {X }n be a sequence of arbitrary random variables with EXn=0 and EX2n <¥، for every n ³ 1 and {a nk} be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also، we will prove complete convergence for weighted sums S nj=1(anjXj)، under some conditions on anj and sequence {Xn، n ³ 1}.