anonymous
  • anonymous
does anyone know about the Fibonacci sequence? :)
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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Callisto
  • Callisto
i think wiki helps you a lot http://en.wikipedia.org/wiki/Fibonacci_number
anonymous
  • anonymous
Today I learned the Fibonacci's sequence closed form expression. :3 I thought it could only be defined as a recurrence.
dumbcow
  • dumbcow
1,1,2,3,5,8,13,21 ...

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dumbcow
  • dumbcow
the ratio of any 2 consecutive terms in the sequence approaches the golden ratio
Callisto
  • Callisto
i read it from a book and found that it's very interesting, but not sure if it is really a 'sequence'
anonymous
  • anonymous
It is a sequnce defined as the next term is the sum of the previous terms. \[x_{n+1}= x_{n}+x_{n-1}\] 1,1,2,3,5,8,13,21,... Solution of this recurrence relation is given here: http://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression
anonymous
  • anonymous
you can't call a sequence a fabbonacci sequence if the sequence of numbers doesn't have common ratio. .
anonymous
  • anonymous
But just because the ratio of terms tends to the golden ratio does not make it a fibaci sequence. See lewis numbers. Oh and Vi Hart has some awesome stuff on fibonacci http://www.youtube.com/watch?v=ahXIMUkSXX0
Callisto
  • Callisto
i think a set of number without common ratio but with common difference can also be called as a sequence... but then it comes to the question of definition of sequence :S
anonymous
  • anonymous
A sequence is just a countable set of numbers. And set of of numbers where you can say this is the first, this is the second etc. There's no need for a common ratio, or any relationship between them.
apoorvk
  • apoorvk
Its is much simpler than what we all have written above... each term is just the sum of the previous two terms.... and coincidentally (or whatever you may like to call it) it also has the golden ratio thingy coming to it.

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