Difference between revisions 3684625 and 3684626 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]]
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: (''n'' + 1) ''F''(0) + ''n'' ''F''(1) + … + ''F''(''n'') = ''F''(''n'' + 2) + ''F''(''n'' + 3) &minus; (''n'' + 3)

Akhir sekali, kita melengkapkan bukti dengan membuat tolakan pengenalan di atas daripada ''n'' + 1 kali pengenalan kedua.

=== 
Fifth IdentityPengenalan Kelima ===

:<math>\sum_{i=0}^n {F_i}^2 = F_{n} F_{n+1}</math>

:''The sum of the first n Fibonacci numbers squared is the product of the nth and (n+1)th Fibonacci numbersJumlah bagi nombor Fibonacci n yang pertama dikuasa dua adalah hasil darab nombor Fibonacci ke-n dan ke-(n+1).''

=== Identity for doubling ''n'' ===

:<math>F_{2n} = F_{n+1}^2 - F_{n-1}^2 = F_n(F_{n+1}+F_{n-1}) </math>

<ref name="autogenerated1">[http://mathworld.wolfram.com/FibonacciNumber.html Fibonacci Number - from Wolfram MathWorld<!-- Bot generated title -->]</ref>

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*[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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