___________________________________________________________
Calculus II Quiz
#8 April
29, 2005
Name_________________ R. Hammack Score
______
___________________________________________________________
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.