Abstarct: One of important theorems in probability theory are limit theorems. Among them large numbers law specific importance. In this law under certain conditions, mean of random variables convergent to it’s expected value. This law has been introduced in 1713. After years, with introduction of negatively associated concept for random variables, many scientists studeied complete convergence for negatively associated random variables. The aim of this thesis is consideration of limit theorems (Strong law of large nimbers) and convergence rate for weight sums of negatively associted random variables. According to importance of strong law of large numbers, we examine complete convergence for weighted sums with considering under different conditions for negatively assicated random variables.