+5265 I can give you about 10-15 numbers in the sequence.
1,1,2,3,5,8,13,21,34,55,89
There's 11. Anyone else want to continue on afterwards?
+129845 The nth Fibonacci number is given by :
F(n) = [ Phi^n - [-phi]^n ] / √ 5
Where Phi = [ 1 + √5] / 2
And phi = 2 / [ 1 + √5 ]
+8262 Well, this is all about adding the number that is before that number with your answer.
FOR EXAMPLE:
1+1=2
2+1=3
3+2=5
5+3=8
and so on.
+26387 What is the whole order of Fibonacci numbers?
\(\text{Golden Ratio } = \varphi \\ \varphi =\frac{ 1+\sqrt{5} } {2}\\ \varphi = 1.61803398875\dots\)
Fibonacci numbers:
\(f_n = \dfrac{ \varphi^n - (1-\varphi)^n } {\sqrt{5}}\)
Sequence below zero:
\(f_{-n} = (-1)^{n+1}\cdot f_n\)
\(\begin{array}{rrrrrrrrrrrrrrrrrrrr} \hline n &=& \dots &-6 &-5 &-4 &-3 &-2 &-1 &0 &1 &2 &3 &4 &5 &6 &\dots \\ \hline f_n &=& \dots &-8 &5 &-3 &2 &-1 &1 &0 &1 &1 &2 &3 &5 &8 &\dots \\ \hline \end{array} \)
