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arXiv · 2601.16770

Sums of Reciprocals of Generalized Triangular Numbers

Pawel Grzegrzolka·Jeffrey L. Meyer
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Abstract

We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized (higher-order) triangular numbers and derive closed-form expressions for both the non-alternating and alternating series of all orders.

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Pawel Grzegrzolka, Jeffrey L. Meyer. 2026-02-04. Sums of Reciprocals of Generalized Triangular Numbers. https://arxiv.org/abs/2601.16770

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