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(-1)* 6k +4 Consider the series k=1 a) Enter the p-series that can be used to determine whether the given series is absolutely convergent, conditionally convergent, or divergent by the Limit Comparison Test. Q To enter the series k-1 F type sum(k, 1, infinity, 1/k^p).

(-1)* 6k +4 Consider the series k=1 a) Enter the p-series that can be used to determine whether the given series is absolutely convergent, conditionally convergent, or divergent by the Limit Comparison Test. Q To enter the series k-1 F type sum(k, 1, infinity, 1/k^p).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) Let bk denote the kn term of the series input in part a). Which of the following statements is true? O The original series is an alternating series with terms that approach 0 and never increase in absolute value, which is inconclusive. Using the Limit Comparison Test to compare the series of absolute values of the original series to b; shows that the original series is divergent. O Using the Limit Comparison Test to compare the series of absolute values of the original series to bk shows that the original series is absolutely convergent. The original series is an alternating series with terms that approach 0 and never increase in absolute value, which is inconclusive. Using the Limit Comparison Test to compare the series of absolute values of the original series to br is also inconclusive. The original series is an alternating series with terms that approach 0 and never increase in absolute value, so it converges. Using the Limit Comparison Test to compare the series of absolute values of the original series to b shows that the original series is conditionally convergent.
Transcribed Image Text:b) Let bk denote the kn term of the series input in part a). Which of the following statements is true? O The original series is an alternating series with terms that approach 0 and never increase in absolute value, which is inconclusive. Using the Limit Comparison Test to compare the series of absolute values of the original series to b; shows that the original series is divergent. O Using the Limit Comparison Test to compare the series of absolute values of the original series to bk shows that the original series is absolutely convergent. The original series is an alternating series with terms that approach 0 and never increase in absolute value, which is inconclusive. Using the Limit Comparison Test to compare the series of absolute values of the original series to br is also inconclusive. The original series is an alternating series with terms that approach 0 and never increase in absolute value, so it converges. Using the Limit Comparison Test to compare the series of absolute values of the original series to b shows that the original series is conditionally convergent.
(-1)* 6k +4 Consider the series k=1 a) Enter the p-series that can be used to determine whether the given series is absolutely convergent, conditionally convergent, or divergent by the Limit Comparison Test. Q To enter the series type sum(k, 1, infinity, 1/k^p). Q QU Su b) Let b denote the k term of the series input in part a). Which of the following statements is true? The original series is an alternating series with terms that approach 0 and never increase in absolute value, which is inconclusive. Using the Limit Comparison Test to compare the series of absolute values of the original series to R shoOws that the original series is divergent. O Using the Limit Comparison Test to compare the series of absolute values of the original series to bị shows that the original series is absolutely convergent.
Transcribed Image Text:(-1)* 6k +4 Consider the series k=1 a) Enter the p-series that can be used to determine whether the given series is absolutely convergent, conditionally convergent, or divergent by the Limit Comparison Test. Q To enter the series type sum(k, 1, infinity, 1/k^p). Q QU Su b) Let b denote the k term of the series input in part a). Which of the following statements is true? The original series is an alternating series with terms that approach 0 and never increase in absolute value, which is inconclusive. Using the Limit Comparison Test to compare the series of absolute values of the original series to R shoOws that the original series is divergent. O Using the Limit Comparison Test to compare the series of absolute values of the original series to bị shows that the original series is absolutely convergent.
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