Fibonacci sequence - calculating values

[Mokae]

Hello,
a couple of days back I have learn about calculating fibonacci sequences but still I don;t quite uderstand the way it is calcilated, could you please give me some thoughts about it?

Thank you

 

[grmnsplx]

it's easy
F_{n+1} = F_{n} + F_{n-1}

So the next number in the series, F_{n+1}, is the sum of the previous two numbers

We start with 1. 1 plus the previous number, 0, is 1. 1+0=1. Now our series is 1,1
Now we take 1 and the number before it, 1 and add. 1+1=2. Now our series is 1,1,2
Now we take 2 and the previous number, 1, and add. 2+1=3. Now our series is 1,1,2,3.
Now take 3 and add the previous number, 2, and add. 3+2=5. 1,1,2,3,5
5+3=8, 8+5=13, 13+8=21, ... Fib Series looks like 1,1,2,3,5,8,13,21,...

got it?

 

[Mokae]

Thank you,
my profesor teach me to use sqrt of 2 plus 5 all divide 2
to calculate and i don't understand why. I am too scare to ask him again

 

[Gib Z]

No, your teacher told you to use \frac{\sqrt{5}+1}{2} to calculate Fibonnaci terms. That constant I just said is the golden ratio, commonly denoted by the greek letter "phi", \phi. It is used in the closed form expression of the terms in the sequence. Don't be asked, you should ask him again.

 

[tiny-tim]

… wikipedia … !

Hi Mokae!

If you don't understand something, wikipedia is usually a good place to look.

For the siginificance of √5 in Fibonacci numbers, look at:

http://en.wikipedia.org/wiki/Fibonacci_number. ​