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Fibonaccish ratio (Posted on 2015-12-07) Difficulty: 3 of 5
It is a very well known mathematical fact that the limiting ratio of consecutive terms of the Fibonacci sequence [F0=0, F1=1, Fn=Fn-1+Fn-2] is Ļ†=(1+āˆš5)/2 as nā†’āˆž.

Suppose we generalize the definition of the sequence to:
Fn=AFn-1+BFn-2.

Find an expression for the limiting ratio of consecutive terms (in terms of A and B.)

Find formulas for A and B to make the limiting ratio any whole number N.

No Solution Yet Submitted by Jer    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): solution Comment 3 of 3 |
(In reply to re: solution by Steve Herman)

a) I did substitute A=1, and show that formula in the middle of the post, with a table of B values to be used for A=1 when N is anywhere from 1 to 10.


b) I took limiting ratio to mean an asymptotic approach, rather than just ask for a geometric sequence.

c) Agreed.

  Posted by Charlie on 2015-12-07 19:54:13
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