The infinites of some divergent series: Los infinitos de algunas series divergentes - Miramontes de León, Diego (2020)
This work aims to show that two divergent series, although both have an infinite number of terms, if they have different terms, their value to infinity also differs. In this document, it is shown that the harmonic series, given by the sum of the inverse of natural numbers, can be decomposed into two series; one of them is given by the sum of the inverse of the naturals in the form 1/np where p > 1 and the other, which will be called subharmonic, formed by the rest of the terms that complete the originalharmonic series. It is shown that each of these series is one convergent and the other divergent, thus obtaining the original divergent series. It is included the demonstration of the divergence of the new series, and as an extension of this decomposition of the harmonic series, a comparison is made of two subharmonic series which, despite being both divergent, differ in their value to infinity.