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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 00 Consider the series Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k= 1 (a) Is this a geometric series, that is, would the geometric series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. This is not a geometric series. O B. This is a geometric series with r = (type an exact value). Since |r|<1, the series CONVERGES. O C. This is a geometric series with r = (type an exact value). Bince | r|21, the series DIVERGES. b) Is this a P-series, that is, would the P-series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. DA. This is not a P-series. D B. This is a P-series with p= (type an exact value). Since ps1, this series DIVERGES, OC. This is a P-series with p = (type an exact value). Since p>1, this series CONVERGES. 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 00 Consider the series Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k= 1 (a) Is this a geometric series, that is, would the geometric series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. This is not a geometric series. O B. This is a geometric series with r = (type an exact value). Since |r|<1, the series CONVERGES. O C. This is a geometric series with r = (type an exact value). Bince | r|21, the series DIVERGES. b) Is this a P-series, that is, would the P-series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. DA. This is not a P-series. D B. This is a P-series with p= (type an exact value). Since ps1, this series DIVERGES, OC. This is a P-series with p = (type an exact value). Since p>1, this series CONVERGES. 3°C Cloudy

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section: Chapter Questions
Problem 6CC
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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 00 Consider the series Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k= 1 (a) Is this a geometric series, that is, would the geometric series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. This is not a geometric series. O B. This is a geometric series with r = (type an exact value). Since |r|<1, the series CONVERGES. O C. This is a geometric series with r = (type an exact value). Bince | r|21, the series DIVERGES. b) Is this a P-series, that is, would the P-series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. DA. This is not a P-series. D B. This is a P-series with p = (type an exact value). Since ps1, this series DIVERGES, OC. This is a P-series with p = (type an exact value). Since p>1, this series CONVERGES. 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 00 Consider the series Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k= 1 (a) Is this a geometric series, that is, would the geometric series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. This is not a geometric series. O B. This is a geometric series with r = (type an exact value). Since |r|<1, the series CONVERGES. O C. This is a geometric series with r = (type an exact value). Bince | r|21, the series DIVERGES. b) Is this a P-series, that is, would the P-series test work? Select the correct choice below and, if necessary, fill in the answer box within your choice. DA. This is not a P-series. D B. This is a P-series with p = (type an exact value). Since ps1, this series DIVERGES, OC. This is a P-series with p = (type an exact value). Since p>1, this series CONVERGES. 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. 00 k2 Consider the series Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k = 1 (c) Would the test for divergence be conclusive here? Select the correct choice below. O A. Since the limit of the terms is zero, the test for divergence shows that this series CONVERGES. O B. Since the limit of the terms is non-zero or does not exist, the test for divergence shows that this series DIVERGES. OC. Since the limit of the terms is zero, the test for divergence is inconclusive. O D. Since the limit of the terms exists and is non-zero, the test for divergence shows that this series CONVERGES. (d) Would the root test be conclusive here? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Applying the root test gives p= (type an exact value, or oo or - c0). Since p >1, the series DIVERGES by the root test. O B. Applying the root test gives p= (type an exact value, or co or – 0). Since p< 1, the series CONVERGES by the root test. O C. Applying the root test gives p= 1. Therefore, the root test is inconclusive. 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. 00 k2 Consider the series Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k = 1 (c) Would the test for divergence be conclusive here? Select the correct choice below. O A. Since the limit of the terms is zero, the test for divergence shows that this series CONVERGES. O B. Since the limit of the terms is non-zero or does not exist, the test for divergence shows that this series DIVERGES. OC. Since the limit of the terms is zero, the test for divergence is inconclusive. O D. Since the limit of the terms exists and is non-zero, the test for divergence shows that this series CONVERGES. (d) Would the root test be conclusive here? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Applying the root test gives p= (type an exact value, or oo or - c0). Since p >1, the series DIVERGES by the root test. O B. Applying the root test gives p= (type an exact value, or co or – 0). Since p< 1, the series CONVERGES by the root test. O C. Applying the root test gives p= 1. Therefore, the root test is inconclusive. 3°C Cloudy
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