Date of Award
Master of Science
Randall G McCutcheon
David P Dwiggins
We investigate the phenomenon of divergent series of positive terms having convergent minimum. As entry into this topic, we look at Exercise twenty-three from chapter two of Karl R. Stromberg’s ”Introduction to Classical Real Analysis”, which addresses this very case. The exercise calls for the construction of two in?nite divergent series, Pan and Pbn, having strictly positive, non-increasing terms, such that the series Pcn, the nth term of which is the minimum of the nth terms of the original two series, converges. We then establish that it is not possible that one of the original two series in such a construction can be the harmonic series. Along the way, we consider Exercise forty-seven, part b from chapter two of the same text, which asks: if we have an in?nite, divergent series Pdn, then what can be said of the in?nite series dn/1+ndn? We also utilize the properties of upper and lower density in formulating the ?nal proof.
dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Russo, Alexander James, "A Study Of Two Divergent Series With A Convergent Minimum" (2019). Electronic Theses and Dissertations. 2016.