fall17mth143.practice2.3-ConvergenceTestsI.pdf

# 2 for all n 1 arctan n n 3 π 2 n 3 and the series π

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2. For all n > 1, arctan ( n ) n 3 < π 2 n 3 , and the series π 2 1 n 3 con- verges, so by the Comparison Test, the series arctan ( n ) n 3 converges. 3. For all n > 1, 1 n ln ( n ) < 2 n , and the series 2 1 n diverges, so by the Comparison Test, the series 1 n ln ( n ) diverges. 4. For all n > 2, 1 n 2 - 3 < 1 n 2 , and the series 1 n 2 converges, so by the Comparison Test, the series 1 n 2 - 3 converges. 5. For all n > 2, ln ( n ) n > 1 n , and the series 1 n diverges, so by the Comparison Test, the series ln ( n ) n diverges. 6. For all n > 2, ln ( n ) n 2 > 1 n 2 , and the series 1 n 2 converges, so by the Comparison Test, the series ln ( n ) n 2 converges. Answer(s) submitted: (incorrect) 4

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Correct Answers: C C I I C I Generated by c WeBWorK, , Mathematical Association of America 5
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