Exercise 7.  In the the proof of Theorem 4.12 regarding geometric series, show that if  ,  then  .  

Solution 7.

See text and/or instructor's solution manual.

Solution.     .

Now use the fact that if  ,  then    to get the desired conclusion

                      

This solution is complements of the authors.

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