 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Fibonaccish ratio (Posted on 2015-12-07) 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 φ=(1+√5)/2 as n→∞.

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 Please log in:

 Search: Search body:
Forums (0)