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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)sums to ''n''&minus;2, so there are ''F''(''n''&minus;1) sums in the second set. The first summand can only be 1 or 2, so these two sets exhaust the original set. Thus ''F''(''n''+1) = ''F''(''n'') + ''F''(''n''&minus;1).

=== Second Identity ===

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

:''
The sum of the first n Fibonacci numbers is the (n+2)nd Fibonacci number minusJumlah bagi n pertama nombor Fibonacci adalah nombor Fibonacci ke-(n+2) tolak 1.''

==== Proof ====

We count the number of ways summing 1's and 2's to ''n'' + 1 such that at least one of the summands is 2.

As before, there are ''F''(''n'' + 2) ways summing 1's and 2's to ''n'' + 1 when ''n'' ≥ 0.
(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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