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=
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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.
Last edited by Jameson; September 9th 2009 at 04:11 PM.
Originally Posted by DeRSeD 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= Start by showing that for n = 0 and n = 1. Then assume for all , where . If so, then If you can show then you will be done. You might want to start by looking at the case k=1.
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