Thesis Defense Announcement

College of Arts and Sciences announces the Final Thesis Defense of

Alexander Russo

for the Degree of Master of Science

April 18, 2019 at 10:00 AM in Dunn Hall, Room 203 

Advisor: Randall McCutcheon

A study of two divergent series with a convergent minimum.

ABSTRACT: Exercise twenty-three from chapter two of Karl R. Stromberg's "Introduction to Classical Real Analysis" addresses this the case of multiple infinite, divergent series of non-negative terms having a convergent minimum. The exercise itself calls for the construction of two infinite divergent series, a_n and b_n, having strictly positive, non-increasing terms, such that the series, c_n, the nth term of which is the minimum of the nth terms of the original two series, converges. We then prove 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 make a connection between this exercise and exercise forty-seven, part b from chapter two of the same text, which poses the question that if we have an infinite, divergent series, d_n, then what can be said of the infinite series d_n/(1+nd_n)? We formulate and establish basic properties of upper and lower density in formulating the main result.