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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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    See http://en.wikipedia.org/wiki/Fibonacci_number#Relation_to_the_golden_ratio2011-12-12
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    It's on the Wikipedia page ^^. What search did you employ that failed to show you this?2011-12-12

2 Answers 2

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The n-th Fibonacci number is given in closed form by

$$F_n=\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^n- \frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^n $$

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    But the OP asked how *how to find* the closed form. See J.M.'s dup link for some answers.2011-12-12
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    Yes sorry but with my tablet is very difficult to post more involved answers.2011-12-12
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This is probably the most expiated discussion of $n$-th term of Fibonacci series in world wide web.

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    Perhaps you should clarify what you mean by an "expiated discussion". IMO the linked page leaves much to be desired.2011-12-12