Difference between revisions 3684616 and 3684618 on mswiki

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Nombor Fibonacci
{{pelbagai isu|{{cleanup|reason=memerlukan penterjemahan segera kerana sudah ditinggalkan sejak tahun 2008|date=Ogos 2014}}{{Terjemah|en|fabonacci number|date=Ogos 2014}}}}
{{proses|BukanTeamBiasa}}
[[Image:FibonacciBlocks.svg|thumb|180px|right|Suatu ubinan dengan segi empat yang tepinya adalah nombor Fibonaci berturut-turut pada panjangnya]]
(contracted; show full)
:<math>\sum_{i=0}^{n-1} F_{2i+1} = F_{2n}</math>
:<math>\sum_{i=0}^{n} F_{2i} = F_{2n+1}-1</math>

<ref>{{cite book | title = Fibonacci Numbers |last = Vorobiev |first = Nikolaĭ Nikolaevich |coauthors = Mircea Martin | publisher = Birkhäuser | year = 2002 | id = ISBN 3-7643-6135-2 |chapter=Chapter 1 |pages = pp. 5–6}}</ref>

:''Jumlah bagi nombor Fibonacci n-1 pertama, <math>F_j</math>, 
bahawsupaya j ganjil adalah nombor Fibonacci ke-(2n).''
:''Jumlah bagi nombor Fibonacci n pertama, <math>F_j</math>, bahawsupaya j genap adalah nombor Fibonacci ke-(2n+1) tolak 1.''

==== Pembuktian ====

Aruhan bagi <math>F_{2n}</math>:
:<math>F_1+F_3+F_5+...+F_{2n-3}+F_{2n-1}=F_{2n}</math>
:<math>F_1+F_3+F_5+...+F_{2n-3}+F_{2n-1}+F_{2n+1}=F_{2n}+F_{2n+1}</math>
:<math>F_1+F_3+F_5+...+F_{2n-3}+F_{2n-1}+F_{2n+1}=F_{2n+2}</math>
(contracted; show full)
*[http://web.archive.org/web/20070715032716/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=630&bodyId=1002 Fibonacci Numbers] at [http://web.archive.org/web/20060212072618/http://mathdl.maa.org/convergence/1/ Convergence]
* [http://www.tools4noobs.com/online_tools/fibonacci/ Online Fibonacci calculator]

[[Kategori:Fibonacci numbers|*]]
[[Kategori:Articles containing proofs]]

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