Example 4.2.  Show that the sequence    diverges.  

Solution.  We have  

              

The real sequences    and    both exhibit divergent oscillations, so we conclude that    diverges.

Explore Solution 4.2.

Enter the formula for the terms of the sequence, and determine if the sequence converges or diverges.

Investigate the limit in more detail.

Therefore, the limit of the sequence does not exist, and exhibits "divergent oscillations."

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

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

We see that the sequence    is divergent.  

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