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PreprintarXiv licencearXiv

The infinite sum of the cubes of reciprocal balancing numbers

  • Subhasis Panda
  • Aditya Kumar Dash
  • Utkal Keshari Dutta
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Abstract

In this paper, we study the infinite reciprocal cubic sum ∑k=n∞1/Bk3 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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Cite

BibTeXRIS
BibTeX
@misc{panda2026infinite,
  title = {{The infinite sum of the cubes of reciprocal balancing numbers}},
  author = {Subhasis Panda and Aditya Kumar Dash and Utkal Keshari Dutta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32815},
  eprint = {2609.32815},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32815},
}
RIS
TY  - UNPB
TI  - The infinite sum of the cubes of reciprocal balancing numbers
AU  - Subhasis Panda
AU  - Aditya Kumar Dash
AU  - Utkal Keshari Dutta
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32815
UR  - https://arxiv.org/abs/2609.32815
AB  - In this paper, we study the infinite reciprocal cubic sum ∑_k=n^∞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.
ER  -