Proving zeta(2) through an evolution of the Mengoli's series to the set of rational numbers

Abstract

The present paper is an evolution of the Mengoli's series to the set of rational numbers, which eventually will allow developing the summation, by limits, obtaining the value of zeta(2); problem which Mengoli himself was the first to postulate. More specifically in this paper is postulated and demonstrated the function which resolves every summation since n=1 to infinite of the type 1/((n+a/w)(n+b/w)...(n+z/w)) for all a,b,...,z,w belonging to the set of integers, where a>b>...>z are different; a/w,b/w,...,z/w not equal to -1,-2,-3,... Finally limits to the past summation is applied to demonstrate zeta(2).