%0 Journal Article
%T Proving zeta(2) through an evolution of the Mengoli's series to the set of rational numbers
%A Uriel Valentinis Ramos
%J Mathematics
%D 2014
%I arXiv
%X 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).
%U http://arxiv.org/abs/1405.1870v1