Abstract
In this paper, we establish a formula for finding the closest integer to the reciprocal of ∑m≥n1/Pm(k) where {Pn(k)}n≥-(k-2) is the k-generalized Pell sequence or the k-Pell sequence given by Pn(k)=2Pn-1(k)+⋯+Pn-k(k)for alln≥2, with initial conditions P-(k-2)(k)=P-(k-3)(k)=⋯=P0(k)=0 and P1(k)=1 . We show that the closest integer to the reciprocal of ∑m≥n1/Pm(k) is given by Pn(k)-Pn-1(k) for every k≥ 2 and for every n≥ 2 .
Original language | English |
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Journal | Indian Journal of Pure and Applied Mathematics |
DOIs | |
Publication status | Accepted/In press - 2023 |
Keywords
- Closest integer
- Linearly recurrent sequences
- Reciprocal sum
- k-generalized Fibonacci numbers
- k-generalized Pell numbers