It is a very well known mathematical fact that the limiting ratio of consecutive terms of the Fibonacci sequence [F
0=0, F
1=1, F
n=F
n-1+F
n-2] is Ļ=(1+ā5)/2 as nāā.
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.
(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.
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Posted by Charlie
on 2015-12-07 19:54:13 |
re(2): solution
