Mathematics, 17.04.2021 19:30 Eni1127
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 Correct if the argument is valid, or enter 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 Incorrect.
1. For all n>1, sin2(n)n2<1n2, and the series β1n2 converges, so by the Comparison Test, the series βsin2(n)n2 converges.
2. For all n>1, arctan(n)n3<Ο2n3, and the series Ο2β1n3 converges, so by the Comparison Test, the series βarctan(n)n3 converges.
3. For all n>2, 1n2β5<1n2, and the series β1n2 converges, so by the Comparison Test, the series β1n2β5 converges.
4. For all n>2, n+1ββββββn>1n, and the series β1n diverges, so by the Comparison Test, the series βn+1ββββββn diverges.
5. For all n>2, nn3β2<2n2, and the series 2β1n2 converges, so by the Comparison Test, the series βnn3β2 converges.
6. For all n>1, n2βn3<1n2, and the series β1n2 converges, so by the Comparison Test, the series βn2βn3
Answers: 3
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Each of the following statements is an attempt to show that a given series is convergent or divergen...
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