BC ONLYExample 17 __
Does the series converge or diverge?
SOLUTION: diverges, because it is a p-series with .
THE COMPARISON TEST
We compare the general term of , the nonnegative series we are
investigating, with the general term of a series, , known to converge or
diverge.
(1) If converges and an un, then converges.
(2) If diverges and an un, then diverges.
Any known series can be used for comparison. Particularly useful are p-series,
which converge if p > 1 but diverge if p 1, and geometric series, which
converge if |r| < 1 but diverge if |r| 1.
Example 18 __
Does converge or diverge?
SOLUTION: Since and the p-series converges, converges
by the Comparison Test.
Example 19 __
Does the series converge or diverge?
SOLUTION: diverges, since