Example 4.20.  The sequence    has  .  
We leave verification of this as an exercise.

Explore Solution 4.20.

In this case the sequence has  1  as its limit, and hence the limit supremum  is also  1.

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

In this case the sequence has  1  as its limit, and hence the limit supremum  is also  1.

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