The Sum of Reciprocals of Polygonal Numbers: A Spreadsheet Based Illustration
This pedagogic note considers the sum of reciprocals of polygonal numbers. Closed form expressions of the sum are currently available for twelve specific cases, from triangles to 26-sided polygons. Several of these expressions are from featured solutions to posted questions in college mathematics jo...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
McMaster University
2025-08-01
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| Series: | Spreadsheets in Education |
| Online Access: | https://sie.scholasticahq.com/article/142984-the-sum-of-reciprocals-of-polygonal-numbers-a-spreadsheet-based-illustration |
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| Summary: | This pedagogic note considers the sum of reciprocals of polygonal numbers. Closed form expressions of the sum are currently available for twelve specific cases, from triangles to 26-sided polygons. Several of these expressions are from featured solutions to posted questions in college mathematics journals. A general expression of the sum, which is in terms of the digamma function and the Euler-Mascheroni constant, is also available for polygons with five sides or more. This note uses an Excel spreadsheet to assess numerically the adequacy of some partial sums and the equivalence of the two analytical approaches. The general expression will be useful for verifying any new additions to the current list of closed form expressions of the sum of the reciprocals of polygonal numbers. |
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| ISSN: | 1448-6156 |