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Calculus  II                                           Quiz #8                     April 29, 2005

Name_________________            R.  Hammack                  Score ______
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Decide if the following series converge or diverge. In the case of convergence, say whether the series converges conditionally or absolutely.

(1)
For k > 1, the series has positive terms.
Further, <<=
Therefore, the series converges by comparison with the convergent p-series
Since it converges and its terms are all positive, then it also converges absolutely.

(2)
Using the ratio test ==== 0
Therefore the series converges. Since the terms are positive, it converges absolutely

(3)
This is an alternating series, with >>>... and == 0.
Therefore it converges by the alternating series test.
However,   || = =+++... is the (divergent) harmonic series (minus the first term).
Therefore the original series converges conditionally.

(4)    -+-+-+ ...
Note that does not exist, for odd terms approach 1 and even terms approach -1.
Therefore the series diverges by the divergence test.