Example 4.1.  Find the limit of the sequence  .  

Solution.  We write  .  Using results concerning sequences of real numbers, we find that  

        and    .  

Therefore  .  

Explore Solution 4.1.

Enter the formula for the terms of the sequence.

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

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

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

We see that the limit of the sequence  .  However, the real part is converging slowly to 0  and the imaginary part is converging a little faster to  .  

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