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Mathematics, 29.02.2020 02:01, ricardodeleon152
Each of the following statements is an attempt to show that a given series is convergent or divergent not 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>2, ln(n)/n>1n, and the series β1/n diverges, so by the Comparison Test, the series βln/(n)n diverges.
2. For all n>1, arctan(n)/n3<Ο2n3, and the series Ο/2β1/n3 converges, so by the Comparison Test, the series βarctan(n)/n3 converges.
3. For all n>1, n/(2βn3)<1n2, and the series β1/n2 converges, so by the Comparison Test, the series βn/(2βn3) converges.
4. For all n>1, ln(n)/n2<1/n1.5, and the series β1/n1.5 converges, so by the Comparison Test, the series βln(n)/n2 converges.
5. For all n>1, 1/nln(n)<2/n, and the series 2β1/n diverges, so by the Comparison Test, the series β1/nln(n) diverges.
6. For all n>2, 1/(n2β7)<1/n2, and the series β1/n2 converges, so by the Comparison Test, the series β1/(n2β7) converges.
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