In this paper we shall describe about the series acceleration for Alternating series . We shall define a correction term and error function for an Alternating series. Using that correction term and error functions, we can deduce a rapidly convergent series. Here we compare the series deduced by Euler transformation method & Aitken’s delta squared process with the series deduced by using correction term and error functions. We will show that our deduced series is better than the other two.