Generalizing Ramaujan Summation

Abstract

Ever since Cesaro introduced the idea of assigning particular value to divergent series of real numbers, various mathematicians had provided novel techniques to assign fixed values for divergent series of real numbers. One such noticeable method is Ramanujan Summation Method. In this paper, we have generalized the notion of Ramanujan Summation method by considering arithmetic progressions. The final result surprisingly provides an alternate form of the original Ramanujan summation method. Several new results regarding Ramanujan summation methods were derived in detail along with suitable figures to enhance the understanding of ideas provided.