Ramanujan summation for geometric progressions

Abstract

Among several summation methods that exist in mathematics, Indian mathematician Srinivasa Ramanujan introduced a novel way of determining sum of divergent series related to Riemann zeta function. In this paper, I extended the idea of Ramanujan summation for Geometric Progressions whose common ratio is greater than 1. In doing so, a general and new result was established in this paper. Using this general result, I had obtained Ramanujan summation of two Geometric Progressions and had also explained the geometric meaning of the answers obtained.