fall17mth143.practice2.3-ConvergenceTestsI.pdf

# Convergesdiverges answers submitted incorrect correct

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[?/Converges/Diverges] Answer(s) submitted: (incorrect) Correct Answers: B Converges B Converges A Diverges D Diverges 9. (1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge. A. n = 1 1 n , B. n = 1 1 n 2 , C. n = 1 1 n 3 , and D. n = 1 1 n 3 / 2 1. n = 1 1 n 3 + 1 Does this series converge or diverge? [?/Converges/Diverges] 3

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2. n = 3 n + 2 ( n + 1 ) 2 Does this series converge or diverge? [?/Converges/Diverges] 3. n = 2 1 2 + n 3 / 2 Does this series converge or diverge? [?/Converges/Diverges] 4. n = 1 n 2 - 1 n 4 + 2 n + 1 Does this series converge or diverge? [?/Converges/Diverges] Answer(s) submitted: (incorrect) Correct Answers: D Converges A Diverges D Converges B Converges 10. (1 point) Consider the series n = 1 11 - n ( An + B ) 3 , with A , B > 0. Does this series converge or diverge? This series [?/converges/diverges]. Answer(s) submitted: (incorrect) Correct Answers: converges 11. (1 point) Test each of the following series for conver- gence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.) 1. n = 1 9 n 4 n 7 + 5 2. n = 1 9 n 4 n 5 + 5 3. n = 1 ( ln ( n )) 3 n + 3 4. n = 1 cos 2 ( n ) n n 4 5. n = 1 cos ( n ) n 9 n + 5 Answer(s) submitted: (incorrect) Correct Answers: CONV DIV DIV CONV NA 12. (1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for ”correct”) if the argument is valid, or enter I (for ”incorrect”) if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) 1. For all n > 1, ln ( n ) n 2 < 1 n 1 . 5 , and the series 1 n 1 . 5 con- verges, so by the Comparison Test, the series ln ( n ) n 2 converges.
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