Fibonacci tricks from Palm Breeze CAFE

Posted by: Gary Ernest Davis on: November 17, 2010

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Here’s the algebra:

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x

x

x

x

x

x

More generally, if $F(n)$ is the $n^{th}$ Fibonacci number, where $F(1)=A, F(2)=B \textrm{ and } F(n+2)=F(n+1)+F(n)$ , and $S(n)$ is the sum of the Fibonacci numbers $F(1)+\ldots+F(n)$ then $S(6+4k)$ Â is an integer multiple of $F(5+2k)$ .

For example, $S(14)=F(1)+\ldots+F(14)=29\times F(9)$ , and $S(98)=F(1)+\ldots+F(98)=17393796001\times F(51)$ .

1 Response to "Fibonacci tricks from Palm Breeze CAFE"

1 | Fibonacci Sequences – the Golden Rule about the Golden Ratio, which we just found out… « Teaching AQA GCSE Maths 2010
November 18, 2010 at 12:16 pm

[…] Our thanks to the Republic of Maths blog that brought this to our attention, via this video link. […]

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