Solution 18 (a).

Solution.   Let      be arbitrary.   

Then,  for   ,   the terms in the series satisfy  

                    .

Since   ,   the series      converges.

Therefore, by the Weierstrass M-test      converges uniformly for  .

Since    was arbitrary,       converges for  .

This solution is complements of the authors.

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