Abstract
In this paper we improve the almost sure behavior of the weighted sum√ by trimming off a fixed number of extreme observations. Let {cn,n>1}and {qn,n>1} be defined by√ and √respectively. Then a sufficient and a necessary conditions for thestablility of the trimmed weighted sum is given under some suitableassumptions on {cn} and {qn}. This also gives an extension of Mori'sstrong laws via letting an=1.