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 > 2, In(n)/n > 1/n , and the series Σ1/n diverges, so by the Comparison Test, the series ΣIn(n)/n diverges .
2. For all n > 2, 1/n2 - 7 > 1/n2 and the series Σ1/n2 converges, so by the Comparison Test, the series Σ1/n2 - 7 converges.
3. For all n > 1, In(n)/n2 < 1/n15, and the series Σ1/n15 converges, so by the Comparison Test, the series ΣIn(n)/n2 converges.
4. For all n > 2, In(n)/n2 <1/n2, and the series Σ1/n2 converges, so by the comparison Test, the series ΣIn(n)/n2 converges.
5. For all n > 1, n/6 - n2 < 1/n2 and the series Σ1/n2 converges, so by the Comparison Test, the series Σn/6 -n2 converges.
6. For all n > 2, n2 - 9 < 2/n2, and the series 2 Σ1/n2 converges, so by the Comparison Test, the series Σn/n2 - 9 converges.