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Consider the series (-1)* k3 + 1" 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. To enter the series E type sum(k, 1, infinity, 1/k^p). 1 Q Qu b) Let b denote the kth term of the series input in part a). Which of the following Su statements is true? The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, which is inconclusive. For k2 1, > br. Since b is convergent, k3 + 1 the Comparison Test is also inconclusive.

Consider the series (-1)* k3 + 1" 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. To enter the series E type sum(k, 1, infinity, 1/k^p). 1 Q Qu b) Let b denote the kth term of the series input in part a). Which of the following Su statements is true? The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, which is inconclusive. For k2 1, > br. Since b is convergent, k3 + 1 the Comparison Test is also inconclusive.

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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Consider the series (-1)* k3 +1" 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. To enter the series 1 L-1 type sum(k, 1, infinity, 1/k^p). Qu b) Let b denote the kth term of the series input in part a). Which of the following Su statements is true? The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, which is inconclusive. For k 1, > bR. Since O is convergent, k3 + 1 the Comparison Test is also inconclusive.
Transcribed Image Text:Consider the series (-1)* k3 +1" 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. To enter the series 1 L-1 type sum(k, 1, infinity, 1/k^p). Qu b) Let b denote the kth term of the series input in part a). Which of the following Su statements is true? The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, which is inconclusive. For k 1, > bR. Since O is convergent, k3 + 1 the Comparison Test is also inconclusive.
b) Let br denote the kh 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. For k 1, > br. Since bk is convergent, k3 + 1 the Comparison Test is also inconclusive. The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, which is inconclusive. For k 1, > bk. Since bk is divergent, the k3 +1 given series is divergent by the Comparison Test. 1 For k > 1, < bk. Since br is convergent, the given series is absolutely convergent k3 +1 by the Comparison Test. O The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, so it converges. For k 21, k3 + 1 bk. Since bk is divergent, the given series is conditionally convergent by the Comparison Test.
Transcribed Image Text:b) Let br denote the kh 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. For k 1, > br. Since bk is convergent, k3 + 1 the Comparison Test is also inconclusive. The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, which is inconclusive. For k 1, > bk. Since bk is divergent, the k3 +1 given series is divergent by the Comparison Test. 1 For k > 1, < bk. Since br is convergent, the given series is absolutely convergent k3 +1 by the Comparison Test. O The original series is an alternating series with terms that approach 0 and never increase in 1 absolute value, so it converges. For k 21, k3 + 1 bk. Since bk is divergent, the given series is conditionally convergent by the Comparison Test.
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