Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers
Abstract:Infinite sums of reciprocals of certain figurate numbers are often discussed in a first-year calculus course. For example, the sum of the reciprocals of the triangular numbers is easily determined since this is an example of a telescoping series. Moreover, the exact value of the sum of the reciprocals of the squares is often mentioned in such courses (with the exact value being 2/6). Unfortunately, little appears in the literature about sums of reciprocals of figurate numbers with more than four sides. Our goal in this capsule is to obtain a closed formula for all such infinite series where the number of sides of the figurate numbers is even and at least six.
Document Type: Miscellaneous
Publication date: 2008-11-01
More about this publication?
- The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. CMJ publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.
- Information for Authors
- Submit a Paper
- Subscribe to this Title
- Membership Information
- Information for Advertisers
- Terms & Conditions
- MAA Journals at ingentaconnect
- MAA Store
- Ingenta Connect is not responsible for the content or availability of external websites