Example 7.2.  Show that      for all   .  

Explore Solution 7.2.

Sum up infinitely many terms to verify that we have things right.

We can use Mathematica to investigate how well the series is "converging" for real numbers.

We can use Mathematica to investigate how well the complex series is "converging" in the complex plane.

Our second exploration is on the disk .
It is an animation of  .

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