webwork.morris.umn.edu Previous Problem Problem List Next Problem point) For each of the series below, select the letter from the possible correct answers A-F that best applies: A. The series is absolutely convergent. B. The series converges but not absolutely. C. The series diverges. D. The alternating series test shows the series converges. E. The series is a P-series. F. The series is a geometric series. We can decide whether this series converges by comparison with P-series. We can decide whether this series converges by comparison with geometric series. Partial sums of the series telescope. The terms of the series do not have a limit of zero. (log(n + 1) / log n) (1+4)^2 (4 - 4) * ((2n-1)/(4 - 1)) * 4^(n+2) * (-1)^n * 6-* dx Note: You can earn partial credit on this problem.
Added by Enrique R.
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(log(n + 1) / log n) We can use the limit comparison test with the p-series 1/n. lim (log(n + 1) / log n) / (1/n) = lim n log(n + 1) / log n = 1 Since the limit is finite and positive, the series is convergent. Answer: B. The series converges but not absolutely. Show more…
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Series Practice: Problem 3 Select the FIRST correct reason why the given series converges. A. Convergent geometric series B. Convergent p-series C. Integral test D. Comparison with a convergent p-series E. Converges by limit comparison test F. Converges by alternating series test
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For each of the series below, select the letter that best applies. Choose the letter that corresponds to the most suitable answer. For example, A represents a series that is absolutely convergent, B represents a series that converges but not absolutely, C represents a series that diverges, and D represents a series that converges according to the alternating series test. The series is a geometric series. We can determine whether this series converges by comparing it with other series. We can also determine whether this series converges by comparing it with a geometric series. The partial sums of the series telescope. The terms of the series do not have a limit of zero. None of the above reasons apply to the convergence or divergence of the series.
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For each of the series below, select the letter from A to K that best applies: A. The series is absolutely convergent. B. The series converges but not absolutely. C. The series diverges. D. The alternating series test shows the series converges. E. The series is a p-series. F. The series is a geometric series. G. We can decide whether this series converges by comparison with a p-series. H. We can decide whether this series converges by comparison with a geometric series. I. Partial sums of the series telescope. J. The terms of the series do not have a limit of zero. K. None of the above reasons applies to the convergence or divergence of the series.
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