8.(1 pt) Each of the following statements is an attempt to3. For alln>1,n6-n3<1n2, and the series∑1n2converges,so by the Comparison Test, the series∑n6-n3converges.4. For alln>1,1nln(n)<2n, and the series 2∑1ndiverges,so by the Comparison Test, the series∑1nln(n)diverges.5. For alln>2,ln(n)n2>1n2, and the series∑1n2converges,so by the Comparison Test, the series∑ln(n)n2converges.6. For alln>1,arctan(n)n3<π2n3, and the seriesπ2∑1n3con-verges, so by the Comparison Test, the series∑arctan(n)n3converges.Correct Answers:•C•C•I•I•I•C9.(1 pt) For each of the series below select the letter fromA to B that best applies and the letter from C to G that bestapplies. For example, if a series is convergent by comparisonwith a p-series type AE for that series.A. The series is convergent.B. The series diverges.C. The series is a p-series.D. The series is a geometric series.E. We can decide whether this series converges by com-parison with a p-series.F. We can decide whether this series converges by com-parison with a geometric series.G. The terms of the series do not have limit zero.1.∞∑n=1cos2(nπ)nπ
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show that a given series is convergent or divergent not using theComparison Test (NOT the Limit Comparison Test.) For eachstatement, enter C (for ”correct”) if the argument is valid, orenter I (for ”incorrect”) if any part of the argument is flawed.(Note: if the conclusion is true but the argument that led to itwas wrong, you must enter I.)1. For alln>1,ln(n)n2<1n1.5, and the series∑1n1.5con-verges, so by the Comparison Test, the series∑ln(n)n2converges.2. For alln>2,nn3-8<2n2, and the series 2∑1n2con-verges, so by the Comparison Test, the series∑nn3-8converges.