MA 124 Exam 2 - Spring '09 Answers
- 1) Converges.
- 2)
- a) Converges (absolutely) by ratio test.
- b) No info on convergence or divergence.
- c) Diverges by ratio test.
- 3)
- a) |R_50| < .02
- b) S_50 < S since the partial sums of an alternating series alternate
above and below the sum S of the series. This partial sum is less than S
since the last term in the partial sum is negative.
- 4) Diverges by the Integral Test.
- 5)
- a) Converges to 1/2 .
- b) Diverges by the n-th term test.
- 6)
- a) Converges to 0.
- b1) Does not converge absolutely by applying the comparison test to
\sum |a_n| and \sum 1/n^(1/2) .
- b2) Converges but not absolutely by alternating series test.
- b3) No, the series does not diverge since it converges by b2).
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