Annales Mathematicae Silesianae (Sep 2019)

Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers

  • Bilgici Göksal,
  • Şentürk Tuncay Deniz

DOI
https://doi.org/10.2478/amsil-2019-0005
Journal volume & issue
Vol. 33, no. 1
pp. 55 – 65

Abstract

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In this paper, we obtain a closed form for F?i=1k${F_{\sum\nolimits_{i = 1}^k {} }}$, P?i=1k${P_{\sum\nolimits_{i = 1}^k {} }}$and J?i=1k${J_{\sum\nolimits_{i = 1}^k {} }}$ for some positive integers k where Fr, Pr and Jr are the rth Fibonacci, Pell and Jacobsthal numbers, respectively. We also give three open problems for the general cases F?i=1n${F_{\sum\nolimits_{i = 1}^n {} }}$, P?i=1n${P_{\sum\nolimits_{i = 1}^n {} }}$ and J?i=1n${J_{\sum\nolimits_{i = 1}^n {} }}$for any arbitrary positive integer n.

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