Question

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 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>1, n/1−n^3<1/n^2, and the series ∑1/n^2∑1/n^2 converges, so by the Comparison Test, the series ∑n/1−n^3 converges.
2. 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.
3. For all n>1, ln(n)/n^2<1/n^1.5 and the series ∑1/n^1.5 converges, so by the Comparison Test, the series ∑ln(n)/n^2 converges.
4. For all n>2, 1/n^2−8<1/n^2, and the series ∑1/n^2 converges, so by the Comparison Test, the series ∑1/n^2−8 converges.
5. For all n>1, 1/nln(n)<2/n, and the series 2∑1/n diverges, so by the Comparison Test, the series ∑1/nln(n) diverges.
6. For all n>1, arctan(n)/n^3<π/2n^3, and the series π2∑1/n^3 converges, so by the Comparison Test, the series ∑arctan(n)/n^3 converges.

Answer 1

久. nu 囚 n (n) Cmves nu, ard, the .21トas Σ_0 Converges, so by ayloen tat hie が-8

21 2n3 Σ끓 conveyo, go.ht (orytorism tat msm tex -1