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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.