Please use this identifier to cite or link to this item:
Title: Lineer indirgeme dizilerinin bazı ters toplamlarının hesaplanması
Other Titles: Evaluation for certain reciprocal sums of linear recurrencesequences
Authors: Kılıç, Emrah
Ersanlı, Didem
Keywords: Ters toplamlar
Basit kesirlere ayırma yöntemi
Teleskop yaratma
Reciprocal sums identities
Partial fraction decomposition
Telescobing idea
Issue Date: 2019
Publisher: TOBB University of Economics and Technology,Graduate School of Engineering and Science
TOBB ETÜ Fen Bilimleri Enstitüsü
Source: Ersanlı, D. (2019). Lineer indirgeme dizilerinin bazı ters toplamlarının hesaplanması. Ankara: TOBB ETÜ Fen Bilimleri Enstitüsü. [Yayınlanmamış yüksek lisans tezi]
Abstract: Bu tezde, $U_{0}=0$, $U_{1}=1$ ve $V_{0}=2$, $V_{1}=p$ başlangıç koşulları olmak üzere her $n\ge{2}$ için \begin{equation*} U_{n}=pU_{n-1}+rU_{n-2}\text{ ve }V_{n}=pV_{n-1}+rV_{n-2}, \end{equation*}% kuralları ile tanımlanan ikinci basamaktan lineer homojen indirgeme dizileri $\lbrace U_{n}\rbrace$ ve $\lbrace V_{n}\rbrace$ ile çalışacağız. Bu dizilerin terimlerini ihtiva eden aşağıdaki ters toplamları hesaplayacağız: \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{V_{k+d+1}}{U_{k+d}U_{k+d+1}U_{k+d+2}}\text{ \ \ \ \ ,\ \ \ \ }\sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k-d}}{U_{k+d}U_{k+d+1}U_{k+d+2}} \end{equation*} ve $X_{n}$, $U_{n}$ ya da $V_{n}$ olmak üzere \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k+c}U_{k+c+1}\ldots U_{k+c+m-1}}{ X_{k+d}X_{k+d+1}\ldots X_{k+d+m+1}}. \end{equation*}
In this thesis, we will consider second order linear homogeneous recurrences $\lbrace U_{n}\rbrace$ and $\lbrace V_{n}\rbrace$ defined by the rules for $n\ge{2}$ \begin{equation*} U_{n}=pU_{n-1}+rU_{n-2}\text{ and }V_{n}=pV_{n-1}+rV_{n-2}, \end{equation*}% where the initial conditions $U_{0}=0$, $U_{1}=1$ and $V_{0}=2$, $V_{1}=p$, respectively. We will evaluate the following reciprocal sums including terms of these sequences \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{V_{k+d+1}}{U_{k+d}U_{k+d+1}U_{k+d+2}}\text{ \ \ \ \ ,\ \ \ \ \ }\sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k-d}}{U_{k+d}U_{k+d+1}U_{k+d+2}} \end{equation*} and \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k+c}U_{k+c+1}\ldots U_{k+c+m-1}}{ X_{k+d}X_{k+d+1}\ldots X_{k+d+m+1}} \end{equation*} where $X_{n}$ is $U_{n}$ or $V_{n}$.
Appears in Collections:Matematik Yüksek Lisans Tezleri / Mathematics Master Theses

Files in This Item:
File Description SizeFormat 
575694 (1).pdfDidem Ersanlı_Tez1.51 MBAdobe PDFThumbnail
Show full item record

CORE Recommender

Page view(s)

checked on Aug 15, 2022


checked on Aug 15, 2022

Google ScholarTM


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.