Ramanujan Summation for Odd and Even Numbered Triangles

Abstract

Pascal’s triangle is the simplest triangle containing binomial coefficients and possessing exclusive mathematical properties in it. There are several triangles of numbers exhibiting exotic mathematical oddities. In this paper, we will introduce two number triangles and determine Ramanujan summation related to their entries. In particular, we have proved new results related to Ramanujan summation values of series of odd and even powers of numbers considered from the two number triangles.