# How to find the closed form to the fibonacci numbers? [duplicate]

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.

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## marked as duplicate by Guess who it is., VelvetThunder, robjohn♦, Martin Sleziak, t.b.Dec 12 '11 at 16:11

–  deinst Dec 12 '11 at 15:46
It's on the Wikipedia page ^^. What search did you employ that failed to show you this? –  The Chaz 2.0 Dec 12 '11 at 15:51

This is probably the most expiated discussion of $n$-th term of Fibonacci series in world wide web.
$$F_n=\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^n- \frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^n$$