PreprintarXiv licencearXiv
On the infinite sum of reciprocals of the fourth powers of balancing numbers
Abstract
In this note, we study the infinite reciprocal sum ∑k=n∞1/Bk4 involving the fourth powers of balancing numbers Bn. We show that, for every n≥2, ⌊ ( ∑k=n∞1/Bk4 )−1 ⌋ = Bn4−Bn−14 −⌈(B2n−1)/280⌉ +εn, where εn=1 if n≡1pmod12 and εn=0 otherwise. This result extends the corresponding reciprocal-sum result for Fibonacci numbers due to Hwang, Park and Song to balancing numbers.
Related
- The infinite sum of the cubes of reciprocal balancing numbers
- Rational Approximations for Reciprocals of Multiple Zeta Values and Trivariate Cauchy Numbers
- On omega-powers of infinite difference rank
- v-numbers of powers of edge ideals of cubic circulant graphs
- Infinite divisibility of powers of positive stable random variables
BibTeX
@misc{panda2026infinite,
title = {{On the infinite sum of reciprocals of the fourth powers of balancing numbers}},
author = {Subhasis Panda and Aditya Kumar Dash and Utkal Keshari Dutta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31548},
eprint = {2609.31548},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31548},
}
RIS
TY - UNPB
TI - On the infinite sum of reciprocals of the fourth powers of balancing numbers
AU - Subhasis Panda
AU - Aditya Kumar Dash
AU - Utkal Keshari Dutta
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31548
UR - https://arxiv.org/abs/2609.31548
AB - In this note, we study the infinite reciprocal sum ∑_k=n^∞1/B_k^4 involving the fourth powers of balancing numbers B_n. We show that, for every n≥2, ⌊ ( ∑_k=n^∞1/B_k^4 )^−1 ⌋ = B_n^4−B_n−1^4 −⌈(B_2n−1)/280⌉ +ε_n, where ε_n=1 if n≡1pmod12 and ε_n=0 otherwise. This result extends the corresponding reciprocal-sum result for Fibonacci numbers due to Hwang, Park and Song to balancing numbers.
ER -