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The infinite sum of the cubes of reciprocal balancing numbers

Subhasis Panda, Aditya Kumar Dash, Utkal Keshari Dutta

Source record

Source: arXiv

Published: Sep 26, 2026

arXiv: 2609.32815

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Source abstract

In this paper, we study the infinite reciprocal cubic sum ∑k=n∞1Bk3\sum_{k=n}^{\infty}\frac{1}{B_k^3} of balancing numbers. We obtain explicit bounds for this sum and use them to determine the integer part of its reciprocal.

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