Some Surprising Series Sums. Issue 1 (1st January 2023)

• Record Type: Journal Article
• Authors: Gordon, Russell A.
• Is Part Of: Mathematics magazine. Volume 96:Issue 1(2023)
• Page Start: 20
• Page End: 29
• Publication Date: 2023-01-01
• Subjects: 40A05; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/0025570X.2023.2168433
• Languages: English
• ISSNs: 0025-570X

Abstract

Summary: We establish the convergence of a family of series for which the usual convergence tests fail. In addition, we show how to use elementary methods to find the sums of the series. A wealth of problems for both calculus students and real analysis students can be obtained from this collection of series and connections can be made to both differential equations and hypergeometric functions.