International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Since Year 2012 | Open Access | Fully Refereed | Peer Reviewed

ISSN: 2319-7064




Downloads: 134 | Monthly Hits: ⮙1

Research Paper | Mathematics | Turkey | Volume 9 Issue 2, February 2020


On the Summations of Some Special Sequences

Kevser Koklu


Abstract: It is well known that many number sequences have important parts in mathematics. Especially in the fields of combinatorics and number theory [15, 16]. Recently, interest has been shown in summing infinite series of reciprocals of some special numbers, for example Fibonacci numbers [5], [6] and [7]. It is not easy, in general, to derive the sum of a series whose terms are reciprocals of Fibonacci, Pell, etc. Numbers such that the subscripts are terms of geometric progressions. It seems even more difficult if the subscripts are in arithmetic progression [13]. Many problems related to the sum of the terms of the Fibonacci series were first proposed in [3]. After that Ken Siler proved the ∑_ (k=1) ^n▒F_ (ak-b) summations provided that a>b in [9]. Single-indexed or double-indexed ones could be summed, for example, some summations of the Pell Quaternions and the Pell-Lucas Quaternions were studied in [2], some summations of the generalized Pell sequence were studied in [10], some summations of the generalized dual Pell and some summations of the generalized dual Pell Quaternions were also studied in [14], but no generalizations were made. In this publication, both these generalizations are made for Pell, Lucas, Pell-Lucas, Jacopsthal, Jacopsthal-Lucas, generalized Pell, generalized dual Pell, and generalized dual Pell quaternion sequences and summing infinite series of reciprocals of the Pell numbers are calculated.


Keywords: Pell number, Lucas number, Pell-Lucas number, Jacopsthal number, Jacopsthal-Lucas number, generalized Pell sequences, generalized dual Pell sequences, generalized dual Pell quaternion sequences


Edition: Volume 9 Issue 2, February 2020,


Pages: 592 - 596

On the Summations of Some Special Sequences


How to Cite this Article?

Kevser Koklu, "On the Summations of Some Special Sequences", International Journal of Science and Research (IJSR), https://www.ijsr.net/get_abstract.php?paper_id=SR20202183933, Volume 9 Issue 2, February 2020, 592 - 596, #ijsrnet

How to Share this Article?

Enter Your Email Address




Similar Articles with Keyword 'Pell'

Downloads: 1

Research Paper, Mathematics, Zambia, Volume 10 Issue 6, June 2021

Pages: 1376 - 1383

Pell-Lucas Series Solution for Fredholm Integral Equations of the Second Kind

Lukonde Peter Alpha

Share this Article

Downloads: 36

Research Paper, Mathematics, Zambia, Volume 10 Issue 2, February 2021

Pages: 1590 - 1598

Pre-School Teacher Subject Matter Knowledge for Teaching Informal Geometry: A Pilot Study

Getrude Chimfwembe- Gondwe | Bentry Nkhata

Share this Article


Top