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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]
Link Posted: 9/29/2004 10:06:48 PM EDT
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?
Link Posted: 9/29/2004 10:09:17 PM EDT
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.
Link Posted: 9/29/2004 10:22:09 PM EDT
Link Posted: 9/29/2004 10:35:49 PM EDT
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.

Link Posted: 9/29/2004 10:39:42 PM EDT
[Last Edit: 9/29/2004 11:04:06 PM EDT by ColonelKlink]
Link Posted: 9/29/2004 11:04:20 PM EDT
Link Posted: 9/30/2004 4:42:08 AM EDT

Originally Posted By ColonelKlink:
gahhh, i give up.




wuss
Link Posted: 9/30/2004 6:14:54 AM EDT
the foregoing explains quite well why I stopped taking math when I stopped being forced to
Link Posted: 9/30/2004 6:17:48 AM EDT
This thread makes my head hurt.
Link Posted: 9/30/2004 9:07:10 AM EDT
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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