The asymptotic estimation for two classes of generalized Fibonacci sub-sequences
Yongkang WAN, Zhonghao LIANG, Qunying LIAO
Received October 15, 2025. Published online April 10, 2026.
Abstract: Since the Fibonacci sequence has good properties, it is important in theory and applications, such as in combinatorics, cryptography, and so on. In this paper, for the generalized Fibonacci sequence $\{W_n(a,b,p,q)\}$, by using elementary methods and techniques, we respectively give the asymptotic estimation values of $\Big({\sum_{k=n}^{\infty}}1/W_{mk+l}^d\Big)^{\!-1}$ and $\Big(\sum_{k=n}^{\infty}(-1)^k/W_{mk+l}^d\Big)^{\!-1}$, which generalize the asymptotic estimation results of H. Li, K. Yang, and P. Yuan (2025).
Keywords: generalized Fibonacci sequence; asymptotic estimation; reciprocal sum
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Affiliations: Yongkang Wan, Zhonghao Liang, Qunying Liao (corresponding author), School of Mathematical Sciences, Sichuan Normal University, Jing'an Road, Jinjiang District 5, 610101 Chengdu, P. R. China, e-mail: 2475636261@qq.com, liangzhongh0807@163.com, qunyingliao@sicnu.edu.cn
