2 (b).  Show that the first series    converges nowhere on  .  

Solution 2 (b).

See text and/or instructor's solution manual.

Solution   A point on    has the polar coordinate form    and   .

In Exercise 9 in Section 4.1 we asked you to prove:   If      converges, then   .   

Use this fact and set  .  

Since    we can conclude that    does not converge.  

Therefore    converges nowhere on  .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell