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Question 3: Series and Convergence (3 points each) a) Use the special series and convergence test...
a) Use the special series and convergence test table to find the sum of the series....
a) Use the special series and convergence test table to find the sum of the series. Be sure to show all work and substitutions. 00 3 8n NO For parts b, c, d, and e, show that the series converges or diverges. The table of special series and convergence tests should be used. Identify the type of convergence test used and be sure to show all work. (Hint: two should diverge) b) 2 + 7 con Σ Test: (-1) in...
30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate wh...
30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate which test you are applying and to show all of your work. (The final exam may include different series that require different convergence tests from the test required in these problems) 3" 2" c) b) n-1 n 2"n e)Σ d) n-2川Inn (2n
30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate which test you are applying and to show...
To test the series e 2n for convergence, you can use the Integral Test. (This is...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
(I point) (a) Check all of the following that are true for the series Σ 2-1 A. This series conver...
(I point) (a) Check all of the following that are true for the series Σ 2-1 A. This series converges B. This series diverges C. The integral test can be used to determine convergence of this series. D. The comparison test can be used to determine convergence of this series. E. The ratio test can be used to determine convergence of this series. F. The alternating series test can be used to determine convergence of this series. (b) Check all...
(1 pt) Test each of the following series for convergence by either the Comparison Test or...
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...
1. or each of the series below, use the divergence test to see i the seies diverges, or state tha...
1. or each of the series below, use the divergence test to see i the seies diverges, or state that the test is inconclusive. 3n 2 2n +1 2. If lim, roan 0 can we always conclude that Σ 1 an converges? If not, give an example showing this fails. 3. Determine if the following p-series converge or diverge. A. TL TL 4. Use the integral test to determine whether the following series converge or diverge. Hint: Use a u-subsitution...
At least one of the answers above is NOT correct (1 point) Test each of the following series for convergence by either...
At least one of the answers above is NOT correct (1 point) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note this mearns that even if you know a given series converges by some other test, but the...
6. One of the following series converges and one diverges. Determine the convergence/divergence of each series....
6. One of the following series converges and one diverges. Determine the convergence/divergence of each series. State which tests that you use. 3n Σ 3" nn n=1 n=1
1 2 3 n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does...
1 2 3
n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
Test for convergence or divergence of the series and identify the test used. In(n) n n...
Test for convergence or divergence of the series and identify the test used. In(n) n n = 2 O diverges by the Direct Comparison Test O converges by the Direct Comparison Test O converges by the p-Series Test O diverges by the p-Series Test Determine the convergence or divergence of the series. (If you need to use co or -, enter INFINITY or -INFINITY, respectively.) 00 į (-1)"(4n – 1) 3n + 1 n = 1 4n - 1 lim...
a) Use the special series and convergence test table to find the sum of the series. Be sure to show all work and substitutions. 00 3 8n NO For parts b, c, d, and e, show that the series converges or diverges. The table of special series and convergence tests should be used. Identify the type of convergence test used and be sure to show all work. (Hint: two should diverge) b) 2 + 7 con Σ Test: (-1) in...
30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate which test you are applying and to show all of your work. (The final exam may include different series that require different convergence tests from the test required in these problems) 3" 2" c) b) n-1 n 2"n e)Σ d) n-2川Inn (2n
30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate which test you are applying and to show...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
(I point) (a) Check all of the following that are true for the series Σ 2-1 A. This series converges B. This series diverges C. The integral test can be used to determine convergence of this series. D. The comparison test can be used to determine convergence of this series. E. The ratio test can be used to determine convergence of this series. F. The alternating series test can be used to determine convergence of this series. (b) Check all...
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...
1. or each of the series below, use the divergence test to see i the seies diverges, or state that the test is inconclusive. 3n 2 2n +1 2. If lim, roan 0 can we always conclude that Σ 1 an converges? If not, give an example showing this fails. 3. Determine if the following p-series converge or diverge. A. TL TL 4. Use the integral test to determine whether the following series converge or diverge. Hint: Use a u-subsitution...
At least one of the answers above is NOT correct (1 point) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note this mearns that even if you know a given series converges by some other test, but the...
6. One of the following series converges and one diverges. Determine the convergence/divergence of each series. State which tests that you use. 3n Σ 3" nn n=1 n=1
1 2 3
n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
Test for convergence or divergence of the series and identify the test used. In(n) n n = 2 O diverges by the Direct Comparison Test O converges by the Direct Comparison Test O converges by the p-Series Test O diverges by the p-Series Test Determine the convergence or divergence of the series. (If you need to use co or -, enter INFINITY or -INFINITY, respectively.) 00 į (-1)"(4n – 1) 3n + 1 n = 1 4n - 1 lim...
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