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Calculus II Quiz
#10 May
4, 2004

Name_________________ R. Hammack Score
______

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Decide if the following series converge or diverge. Use any applicable test.

(1)

The terms are positive, and ,

so it converges by comparison with the
convergent p-series
.

(2)

This is an alternating series that meets the conditions of the Alternating Series
Test, so it CONVERGES.

(3)

Let's try the ratio test for absolute convergence.

Since ,
the original series converges absolutely, so it CONVERGES

(4)

Let's test for absolute convergence, so we look at the positive term series .

Now, ,
so it converges by comparison with the convergent p-series
.

Therefore the original series is absolutely convergent, so it CONVERGES.