000			03182nam a2200433 i 4500
999			_c200437719 _d55931
003			TR-AnTOB
005			20230908000945.0
007			ta
008			171111s2019 xxu e mmmm 00| 0 eng d
035			_a(TR-AnTOB)200437719
040			_aTR-AnTOB _beng _erda _cTR-AnTOB
041	0		_atur
099			_aTEZ TOBB FBE MAT YL’19 ERS
100	1		_aErsanlı, Didem _eauthor _9126712
245	1	0	_aLineer indirgeme dizilerinin bazı ters toplamlarının hesaplanması / _cDidem Ersanlı ; thesis advisor Emrah Kılıç.
246	1	1	_aEvaluation for certain reciprocal sums of linear recurrencesequences
264		1	_aAnkara : _bTOBB ETÜ Fen Bilimleri Enstitüsü, _c2019.
300			_aix, 41 pages : _billustrations ; _c29 cm
336			_2rdacontent _btxt _atext
337			_2rdamedia _bn _aunmediated
338			_2rdacarrier _bnc _avolume
502			_aTez (Yüksek Lisans)--TOBB ETÜ Fen Bilimleri Enstitüsü Temmuz 2019
520			_aBu 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*}
520			_aIn 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 $V_{n}$.
650		7	_aTezler, Akademik _932546
653			_aTers toplamlar
653			_aBasit kesirlere ayırma yöntemi
653			_aTeleskop yaratma
653			_aq-Analiz
653			_aReciprocal sums identities
653			_aPartial fraction decomposition
653			_aTelescobing idea
653			_aq-Calculus
700	1		_aKılıç, Emrah _eadvisor _9126713
710			_aTOBB Ekonomi ve Teknoloji Üniversitesi. _bFen Bilimleri Enstitüsü _977078
856	4	0	_uhttps://tez.yok.gov.tr/ _3Ulusal Tez Merkezi
942			_cTEZ _2z