Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers
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AbstractIn this paper, we obtain a closed form for ${F_{\sum\nolimits_{i = 1}^k {} }}$, ${P_{\sum\nolimits_{i = 1}^k {} }}$and ${J_{\sum\nolimits_{i = 1}^k {} }}$ 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 ${F_{\sum\nolimits_{i = 1}^n {} }}$, ${P_{\sum\nolimits_{i = 1}^n {} }}$ and ${J_{\sum\nolimits_{i = 1}^n {} }}$for any arbitrary positive integer n.
2009 ◽
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pp. 41-53
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1991 ◽
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pp. 457-462
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1961 ◽
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2021 ◽
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pp. 380-395
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