Test each of the following series for convergence 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.)

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3n CONV 1. n° + 10 (In(n)) 2. CONV n+4 cos(n)/n NA 3. Зп + 10 3n DIV 4. no + 10 cos (n) /n CONV 5. Note: In order to get credit for this problem all answers must be correct. preview answers Problem 14. (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 (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, In(n) <+, and the series converges, so by the Comparison Test, the series Σ In(n) converges. 2. For all n>1, 2-n , and the series E converges, so by the Comparison Test, the series 2 converges. In(n) 3. For all n > 2, 1. and the series E diverges, so by the Comparison Test, the series In(n) diverges. , and the series 2E diverges, so by the Comparison Test, the series C 4. For all n > 1, n In(n) Σ diverges. n In(n) In(n) 5. For all n > 2, , and the series converges, so by the Comparison Test, the series In(n) converges. 6. For ail n > 2, , <2, and the series 2 + converges, so by the Comparison Test, the series n-2 2, converges. 3n CONV 1. n° + 10 (In(n)) 2. CONV n+4 cos(n)/n NA 3. Зп + 10 3n DIV 4. no + 10 cos (n) /n CONV 5. Note: In order to get credit for this problem all answers must be correct. preview answers Problem 14. (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 (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, In(n) <+, and the series converges, so by the Comparison Test, the series Σ In(n) converges. 2. For all n>1, 2-n , and the series E converges, so by the Comparison Test, the series 2 converges. In(n) 3. For all n > 2, 1. and the series E diverges, so by the Comparison Test, the series In(n) diverges. , and the series 2E diverges, so by the Comparison Test, the series C 4. For all n > 1, n In(n) Σ diverges. n In(n) In(n) 5. For all n > 2, , and the series converges, so by the Comparison Test, the series In(n) converges. 6. For ail n > 2, , <2, and the series 2 + converges, so by the Comparison Test, the series n-2 2, converges.

Answer rating: 100% (QA)

INA Since half the terms are allor nating seruies so we us... View the full answer