The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences

2025/09/18 by Wan, Yongkang, Liang, Zhonghao, Qunying Liao +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.14569

openalex publication_date 2025/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, for the generalized Fibonacci sequence \W_n(a,b,p,q)\, by using elementary methods and techniques, we give the asymptotic estimation values of (∑_k=n^∞\frac1∑_i=0^ts_iW_mk+li)^-1 and (∑_k=n^∞\frac(-1)^k∑_i=0^ts_iW_mk+li)^-1, respectively. In particular, for some special a,b,p,q,m,t,s_i and l_i(0≤ i≤ t ), Theorem \reftheorem 3.1 is just Theorems 2.1, 2.5-2.6 in \citeA22 given by Yuan et al.

Citations

• On the sum of reciprocal generalized Fibonacci numbers

Related

• The asymptotic estimation for two classes of generalized Fibonacci sub-sequences
• On the sum of reciprocal generalized Fibonacci numbers
• Weighted generalized Fibonacci sums
• Fibonacci Numbers as Sums of Consecutive Terms in k-Generalized Fibonacci Sequence
• Evaluation of weighted Fibonacci sums of a certain type