How can it be proved by induction that the Fibonaaci series is always:

Fn <= ( (1 +sqrt 5)/2 )^(n−1).

F0 = 0, F1 = 1, Fn+2 = Fn+1 + Fn, for n = 0, 1, 2, . . .

golden ratio= http://upload.wikimedia.org/math/7/f...ab1e8044aa.png

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- September 9th 2009, 12:31 PMDeRSeDWhy is Fibonacci =< golden ration^n-1
How can it be proved by induction that the Fibonaaci series is always:

Fn <= ( (1 +sqrt 5)/2 )^(n−1).

F0 = 0, F1 = 1, Fn+2 = Fn+1 + Fn, for n = 0, 1, 2, . . .

golden ratio= http://upload.wikimedia.org/math/7/f...ab1e8044aa.png - September 9th 2009, 02:24 PMJameson
I don't know if you can just use the well-known formula for the nth term of the Fibonacci sequence, but if not you can find a derivation here as well as some other identities.

- September 10th 2009, 06:26 PMawkward