Three conditionally convergent series

TL;DR

The paper proves that for any three conditionally convergent series, a sequence exists making each subseries diverge to infinity or negative infinity, but this does not hold for four series.

Contribution

It establishes a new result about the divergence behavior of subseries of three conditionally convergent series, with a counterexample for four series.

Findings

Existence of a sequence for three series with divergent subseries

Counterexample showing the statement fails for four series

Insight into the structure of conditionally convergent series

Abstract

It is proved that given any three conditionally convergent series of real numbers, there is a single sequence of natural numbers such that each of the corresponding three subseries sums to either $\infty$ or $-\infty$. An example is provided to show that the analogous statement for four series is false.