Ramanujan Summation for Pascal's Triangle

Abstract

The concept of Pascal's triangle has fascinated not only professional mathematicians but also everyone interested in exploring science. Similarly, the idea of Ramanujan summation has made a revolution in mathematical research after it was introduced by Srinivasa Ramanujan. In this paper, we will provide the Ramanujan summation methods for numbers located in slant diagonals of Pascal's triangle and derive a generalized formula for such summations.