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Posted: 9/29/2004 10:03:45 PM EDT
[Last Edit: 9/29/2004 10:03:55 PM EDT by ColonelKlink]
Ok I just started taking calculus 3 which is going over infinite sequences & series, power series, etc.
I got an A in differential calculus and a B+ in integral calc, but this shit is way over my head for some reason. Its way too proof oriented and I suck majorly at that shit. Anyways I got this problem. If you take sucessive ratios of of the terms of the fibonacci sequence it converges to the golden mean at infinity. I am suppose to find the appropriate N value of this sequence if e(thats sposed to be an epsilon) is equal to some arbitrary number, say e=.0001. The problem with this is how the fuck am I suppose to define a limit if I cant even write a formula for the fibonacci sequence cause its simply the sum of the last two terms I cant very well say infinity1 + infinity 2. WTF DO I DO IM SCREWED. Im gonna have to tell my prof that my dog ate my homework. I need help or a point in the right direction, im desperate. 

I am Thor, Supreme Commander of the Asgard fleet. Your presence here is a violation of the Protected Planets Treaty and you must withdraw immediately.

mathworld.wolfram.com/FibonacciNumber.html
to summarize, there is a closed form: Arfcom, home of obscure math answers at 2am......now can someone help me with my menicus reading? 


I dont know how you're supposed to find a limit, but that's pretty cool. I can see what you're describing, never saw that before.


"All truth passes through three stages: first, it is ridiculed; next it is violently attacked; finally, it is held to be selfevident."  Schopenhauer

Yeah but i dont understand how the hell you are suppose to find the N for the e=.0001 of the goldean mean sequence of ratios {1/1,1/2,2/3,3/5,5/8,8/13,13/21}


I am Thor, Supreme Commander of the Asgard fleet. Your presence here is a violation of the Protected Planets Treaty and you must withdraw immediately.

okay, so i'm assuming e = F(n+1)/F(n)  golden ratio? that is, difference from golden ratio of the ratio of the nth and n+1th fibonnaci number? So to show convergence you want to show for N big enough that e is smaller than any given number?
then take the ratio F(n+1)/F(n) given by the closed formula i posted. result won't be pretty, but i think there should be a way to simplify it. Subtract the golden ratio.....and figure out a big enough N to make the whole mess less than epsilon. 


thank you holy shit this is hard. 

I am Thor, Supreme Commander of the Asgard fleet. Your presence here is a violation of the Protected Planets Treaty and you must withdraw immediately.

gahhh, i give up.


I am Thor, Supreme Commander of the Asgard fleet. Your presence here is a violation of the Protected Planets Treaty and you must withdraw immediately.

wuss 

I want to put methamphetamine vending machines in every school cafeteria.
 AR15fan 
the foregoing explains quite well why I stopped taking math when I stopped being forced to



This thread makes my head hurt.



Ah, the Fibonacci sequence. They use it to teach recursion in virtually ever CS program I have seen.
Never had much use for it since. 


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