How to find the closed form to the fibonacci numbers?

Question

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Prove this formula for the Fibonacci Sequence

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.

See http://en.wikipedia.org/wiki/Fibonacci_number#Relation_to_the_golden_ratio — 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

score 0 · Answer 1 · answered Dec 12 '11 at 16:02

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This is probably the most expiated discussion of $n$-th term of Fibonacci series in world wide web.

answered Dec 12 '11 at 16:02

Quixotic

3

Perhaps you should clarify what you mean by an "expiated discussion". IMO the linked page leaves much to be desired. – Bill Dubuque Dec 12 '11 at 16:52

1 Answers1