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8 Answ 9. k = 1

8 Answ 9. k = 1

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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The issue of convergence or divergence of some series can be answered by several k2 Consider the series > Answer the questions below regarding some of the tests one might try in order to determine whe k = 1 O A. Applying the ratio test gives r= 1. Therefore, the ratio test is inconclusive. O B. Applying the ratio test gives r= (type an exact value, or oo or oo). Since r< 1, the series CONVERGES by the ratio tes O C. Applying the ratio test givesrD (type an exact value, or o or - o0). Since r > 1, the series DIVERGES by the ratio test. (f) Can the alternating series test be applied here? Select the correct choice below and, if necessary, fill in the answer box within you O A. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing a CONVERGES by the alternating series test. O B. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing b by the alternating series test. O C. This isn't an alternating series, and therefore we cannot apply the alternating series test. 3°C Cloudy
Transcribed Image Text:The issue of convergence or divergence of some series can be answered by several k2 Consider the series > Answer the questions below regarding some of the tests one might try in order to determine whe k = 1 O A. Applying the ratio test gives r= 1. Therefore, the ratio test is inconclusive. O B. Applying the ratio test gives r= (type an exact value, or oo or oo). Since r< 1, the series CONVERGES by the ratio tes O C. Applying the ratio test givesrD (type an exact value, or o or - o0). Since r > 1, the series DIVERGES by the ratio test. (f) Can the alternating series test be applied here? Select the correct choice below and, if necessary, fill in the answer box within you O A. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing a CONVERGES by the alternating series test. O B. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing b by the alternating series test. O C. This isn't an alternating series, and therefore we cannot apply the alternating series test. 3°C Cloudy
The issue of convergence or divergence of some series can be answered by several different approaches (series tests), and each would give the answer independently. k2 Consider the series E- Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k = 1 (e) Would the ratio test be conclusive here? Select the correct choice below and, it necessary, till in the answer box within your choice. O A. Applying the ratio test gives r= 1. Therefore, the ratio test is inconclusive. O B. Applying the ratio test gives r= (type an exact value, or o or – o0). Since r< 1, the series CONVERGES by the ratio test. O C. Applying the ratio test gives r= (type an exact value, or oo or - c0). Since r> 1, the series DIVERGES by the ratio test. (f) Can the alternating series test be applied here? Select the correct choice below and, if necessary, fill in the answer box within your choice. For this one, we let a, be the m O A. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing and that lim a, : (type an exact value CONVERGES by the alternating series test. O B. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing but that lim a, = (type an exact value, by the alternating series test. ko 3°C Cloudy
Transcribed Image Text:The issue of convergence or divergence of some series can be answered by several different approaches (series tests), and each would give the answer independently. k2 Consider the series E- Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k = 1 (e) Would the ratio test be conclusive here? Select the correct choice below and, it necessary, till in the answer box within your choice. O A. Applying the ratio test gives r= 1. Therefore, the ratio test is inconclusive. O B. Applying the ratio test gives r= (type an exact value, or o or – o0). Since r< 1, the series CONVERGES by the ratio test. O C. Applying the ratio test gives r= (type an exact value, or oo or - c0). Since r> 1, the series DIVERGES by the ratio test. (f) Can the alternating series test be applied here? Select the correct choice below and, if necessary, fill in the answer box within your choice. For this one, we let a, be the m O A. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing and that lim a, : (type an exact value CONVERGES by the alternating series test. O B. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing but that lim a, = (type an exact value, by the alternating series test. ko 3°C Cloudy
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