Possible Duplicate:
Prove this formula for the Fibonacci Sequence
How to find the closed form to the fibonacci numbers?
I have seen is possible calculate the fibonacci numbers without recursion, but, how can I find this formula? Where it come from?
Appreciate helps, thx.
$\endgroup$ 22 Answers
$\begingroup$The n-th Fibonacci number is given in closed form by
$$F_n=\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^n- \frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^n $$
$\endgroup$ 2 $\begingroup$This is probably the most expiated discussion of $n$-th term of Fibonacci series in world wide web.
$\endgroup$ 1
