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Mathematics, 05.08.2020 05:01 diamondalize21p84czi

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. a. For all n>2, ln(n)/n>1n, and the series βˆ‘1/n diverges, so by the Comparison Test, the series βˆ‘ln/(n)n diverges. b. For all n>1, arctan(n)/n3<Ο€2n3, and the series Ο€/2βˆ‘1/n3 converges, so by the Comparison Test, the series βˆ‘arctan(n)/n3 converges. c. For all n>1, n/(2βˆ’n3)<1n2, and the series βˆ‘1/n2 converges, so by the Comparison Test, the series βˆ‘n/(2βˆ’n3) converges. d. For all n>1, ln(n)/n2<1/n1.5, and the series βˆ‘1/n1.5 converges, so by the Comparison Test, the series βˆ‘ln(n)/n2 converges. e. For all n>1, 1/nln(n)<2/n, and the series 2βˆ‘1/n diverges, so by the Comparison Test, the series βˆ‘1/nln(n) diverges. f. For all n>2, 1/(n2βˆ’7)<1/n2, and the series βˆ‘1/n2 converges, so by the Comparison Test, the series βˆ‘1/(n2βˆ’7) converges.

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