@article{387b37bb6e4043359eccb1787f77af92,
title = "Asymptotic behavior of reciprocal sum of two products of Fibonacci numbers",
abstract = "Let {fk}k=1∞ be a Fibonacci sequence with f1= f2= 1. In this paper, we find a simple form gn such that limn→∞{(∑k=n∞ak)−1−gn}=0, where ak=1fk2, 1fkfk+m, or 1f3k2. For example, we show that limn→∞{(∑k=n∞1f3k2)−1−(f3n2−f3n−32+49(−1)n)}=0.",
keywords = "Catalan{\textquoteright}s identity, Convergent series, Fibonacci number, Reciprocal sum",
author = "Lee, {Ho Hyeong} and Park, {Jong Do}",
note = "Funding Information: This work was supported by NRF-2018R1D1A1B07050044 from the National Research Foundation of Korea. Acknowledgements Availability of data and materials Publisher Copyright: {\textcopyright} 2020, The Author(s).",
year = "2020",
doi = "10.1186/s13660-020-02359-z",
language = "English",
volume = "2020",
journal = "Journal of Inequalities and Applications",
issn = "1025-5834",
publisher = "Springer Open",
number = "1",
}