Divergent Series and Its Assigned Value in a Hyperreal Context

Abstract

This letter discusses the deep connection between the infinite sum of natural numbers and the value -1/12. Aside of more widely known facts, we consider a nontrivial way in which we show the veracity of this connection; more precisely this concerns the BGN method \citep{bgn} applied on the so-called damped oscillated Abel summed variant of the series. Moreover, we have found a generalization of this method which `correctly' assigns finite values to other divergent series. We conclude with some questions concerning whether and how we can analytically relate our hyperreal terms to frame the method in a more justifiable and applicable context.