Solution 15 (b).

Answer.      is valid for  .   

Solution.   Solution.   Given  .  

Use the geometric series      which is valid for   ,   

and also the geometric series      which is valid for   .  

Make the substitutions  ,  respectively, and get the following two representations:  

                    ,   valid for   ,   and    

                    ,   valid for   .  

Then     

                       


Therefore,       is valid for  .   

This solution is complements of the authors.

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