Solution 7 (a).

See text and/or instructor's solution manual.

Answer.   .  

Solution.   Given the power series   .  

By Taylor's Theorem,  .  

Therefore,   ,   so that   

                    .  

We are done.   

We can expand the series in its even and odd terms

                    

We are really done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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