Each of the following statements is an attempt to show that a given series is co

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.) For all n 1, arctan(n)/n3 pi /2n3, and the series pi /2 1/n3 converges, so by the Comparison Test, the series arctan(n)/n3 converges. For all n 2, 1/n2-2 1/n2, and the series 1/n2 converges, so by the Comparison Test, the series 1/n2-2 converges. For all n 2, n/n3-5 2/n2, and the series 2 1/n2 converges, so by the Comparison Test, the series n/n3-5 converges. For all n 1, ln(n)/n2 1/n1.5, and the series 1/n1.5 converges, so by the Comparison Test, the series ln(n)/n2 converges. 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. For all n 1, 1/n ln(n) 2/n, and the series 2 1/n diverges, so by the Comparison Test, the series 1/n ln(n) diverges. Match each of the following with the correct statement. The series is absolutely convergent. The series converges, but is not absolutely convergent. The series diverges. infinity n=1 (-7)n/n3 infinity n=1 sin(2n)/n2 infinity n=1 (-1)n n/n + 9 infinity n=1 (-1)n/7n+3 infinity n=1 (n+1)(22 - 1)n/22n For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example. The series is absolutely convergent. The series converges, but not absolutely. The series diverges. The alternating series test shows the series converges. The series is a p-series. The series is a geometric series. We can decide whether this series converges by comparison with a p-series. We can decide whether this series converges by comparison with a geometric series. Partial sums of the series telescope. The terms of the series do not have limit zero. None of the above reasons applies to the convergence or divergence of the series. infinity n=1 (2n+3)!/(n!)2 infinity n=1 cos2(n pi )/n pi infinity n=2 1/nlog(3+n) infinity n=1 1/n n infinity n=1 6+sin(n)/ n infinity n=1 cos(n pi )/n pi Match each of the following with the correct statement. The series is absolutely convergent. The series converges, but is not absolutely convergent. The series diverges. infinity n=1 (-1)n n!/3n infinity n=1 (n+2)!/10nn! infinity n=1 n2/4n infinity n=1 (-1)n3n-1/(3)n+1n1/4 infinity n=1 (-1)n/3nn!

Explanation / Answer

C A C C D

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.