Example 53 __
Use a series to evaluate .
SOLUTION:
From series (1),
BC ONLYThen
a well-established result obtained previously.
Example 54 __
Use a series to evaluate .
SOLUTION: We can use series (4), and write
Example 55 __
Example 56 __
Show how a series may be used to evaluate π.
SOLUTION: Since , a series for tan−^1 x may prove helpful. Note that