Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers
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...
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| Format: | Article |
| Language: | English |
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Sciendo
2019-09-01
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| Series: | Annales Mathematicae Silesianae |
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| Online Access: | http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0005/amsil-2019-0005.xml?format=INT |
| _version_ | 1818210102685990912 |
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| author | Bilgici Göksal Şentürk Tuncay Deniz |
| author_facet | Bilgici Göksal Şentürk Tuncay Deniz |
| author_sort | Bilgici Göksal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T05:11:16Z |
| format | Article |
| id | doaj.art-d525303f3fa0420594152db006e72144 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-12-12T05:11:16Z |
| publishDate | 2019-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-d525303f3fa0420594152db006e721442022-12-22T00:36:54ZengSciendoAnnales Mathematicae Silesianae2391-42382019-09-01331556510.2478/amsil-2019-0005amsil-2019-0005Some Addition Formulas for Fibonacci, Pell and Jacobsthal NumbersBilgici Göksal0Şentürk Tuncay Deniz1Department of Computer Education and Instructional Technologies, Kastamonu University, 37200, KastamonuTurkeyDepartment of Mathematics Institute of Science and Technology, Kastamonu University, 37150, KastamonuTurkeyIn 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.http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0005/amsil-2019-0005.xml?format=INTFibonacci numbersPell numbersJacobsthal numbers11B3911K3111Y55 |
| spellingShingle | Bilgici Göksal Şentürk Tuncay Deniz Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers Annales Mathematicae Silesianae Fibonacci numbers Pell numbers Jacobsthal numbers 11B39 11K31 11Y55 |
| title | Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers |
| title_full | Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers |
| title_fullStr | Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers |
| title_full_unstemmed | Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers |
| title_short | Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers |
| title_sort | some addition formulas for fibonacci pell and jacobsthal numbers |
| topic | Fibonacci numbers Pell numbers Jacobsthal numbers 11B39 11K31 11Y55 |
| url | http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0005/amsil-2019-0005.xml?format=INT |
| work_keys_str_mv | AT bilgicigoksal someadditionformulasforfibonaccipellandjacobsthalnumbers AT senturktuncaydeniz someadditionformulasforfibonaccipellandjacobsthalnumbers |