Rearrangements of a Conditionally Convergent Series Summing to Logarithms of Natural Numbers.

This article explores the concept of rearranging conditionally convergent series to converge to different sums. It provides examples of such rearrangements that are suitable for calculus and undergraduate analysis students. The article compares these rearranged series to the alternating harmonic series and shows that they have the same limit. It also discusses Abel's theorem on power series and its application to the convergence of a specific series, demonstrating that it converges to ln(k). The article concludes by discussing the usefulness of these rearrangements in calculus and analysis classes and acknowledges the contributions of the editorial board and a colleague. [Extracted from the article]