Exercise 5.  Show that   .  

Solution 5.

See text and/or instructor's solution manual.

Solution.  This is a "telescoping sum" and the partial sum is

          

          

          

Then compute the limit of    as follows:

            

Therefore   .  

We are done.   

Aside.  The first 10 partial sums are:  

                    

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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