Example 4.19.  The limit supremum of the Fibonacci sequence    is   .  

(The Fibonacci sequence satisfies the relation    for  ).  

Explore Solution 4.19.

In this case the sequence has    as its limit, and hence the limit supremum  is also  .  

Use Mathematica to plot some of the terms in the sequence.

We see that the limit supremum of the Fibonacci sequence is  .  

(c) 2006 John H. Mathews, Russell W. Howell