Sums of Reciprocals of Generalized Triangular Numbers

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.

arXiv comment14 pages