F(n) is defined as a sequence of positive integers such that F(0) = 0, F(1) = 1, and everything else is determined by the following recurrence relation: F(n) = F(n-1) + F(n-2)

Prove that $$F(n) \leq \phi^{n-1}$$where$$\phi = \frac{1+\sqrt{5}}{2}$$

Question

F(n) is defined as a sequence of positive integers such that F(0) = 0, F(1) = 1, and everything else is determined by the following recurrence relation: F(n) = F(n-1) + F(n-2)

Prove that $$F(n) \leq \phi^{n-1}$$where$$\phi = \frac{1+\sqrt{5}}{2}$$

anonymous · Answer

oh and use induction :-D

anonymous · Answer

are you answering questions for other people or something?

anonymous · Answer

no these are from the text

anonymous · Answer

what text

anonymous · Answer

Inductive prove are highly un-intuitive in my opinion.

anonymous · Answer

http://www.amazon.com/Computer-Programming-Volumes-1-4A-Boxed/dp/0321751043/ref=dp_ob_title_bk

anonymous · Answer

last night you were asking about 3 different C programs, a python program that you'd copied off the web and didn't understand, Pascal's wager, and a bunch of optimization questions.  i'm trying to figure out what's going on, are you doing other people's homework or something?

anonymous · Answer

agd .. without meaning any offence I would like to point out that you may be jumping around many subject very quickly and this may be not be good .. and might lead to cognitive overflow .. happened to me once so I know it sucks!

anonymous · Answer

I think induction is suited for this question.

anonymous · Answer

hmm right...

anonymous · Answer

if I don't take care of myself, tomorrow you might find me asking Bio questions here :-P

anonymous · Answer

hehe, what do you study ?

anonymous · Answer

what school are you at?

anonymous · Answer

:(

anonymous · Answer

what happen .. why are you sad ?

anonymous · Answer

okay how much have you studied ? What do you want to study in future ?

anonymous · Answer

I wanna study medicine!

anonymous · Answer

i don't understand why you're being so evasive... you said you were working with professors at a university yesterday.  which one?

anonymous · Answer

a few, but often with the humanities, or whatever you call the department the professors who give classes writing assignments are in.

anonymous · Answer

i mean which university

anonymous · Answer

binet's formula try here http://fabulousfibonacci.com/portal/index.php?option=com_content&view=article&id=22&Itemid=22 or here http://fabulousfibonacci.com/portal/index.php?option=com_content&view=article&id=22&Itemid=22 or here http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibformproof.html