Example 4.24.  Show that      for all  

Solution.  We know from Theorem 4.12 that    for all  .  If we set k=1 in Theorem 4.16, part (ii), then

              ,

for all  .

Explore Solution 4.24.

Use the fact that    and  .  

Or sum the infinite series directly.

(c) 2006 John H. Mathews, Russell W. Howell