7. Use any method to determine if the series converges or diverges. Give reasons for your answer. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series diverges because the limit used in the nth-Term Test is O B. The Comparison Test with M 8 2n - shows that the series diverges. n= 1 M 8 O C. The Comparison Test with shows that the series converges. n = 1 O D. The series converges per the Integral Test because dx converges. 8. Use any method to determine if the series converges or diverges. Give reasons for your answer. M 8 (n +3)! n = 1 3!n!30 Select the correct choice below and fill in the answer box to complete your choice. O A. The series converges because the limit used in the nth-Term Test is O B. The series diverges because the limit used in the Ratio Test is O C. The series converges because the limit used in the Ratio Test is O D. The series diverges because the limit used in the nth-Term Test is 9. Use any method to determine if the series converges or diverges. Give reasons for your answer. (n!) " M (3n)! Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The series diverges because the limit used in the nth-Term Test is O B. The series converges because the limit used in the nth-Term Test is O C. The series diverges because the limit used in the Ratio Test is O D. The series converges because the limit used in the Root Test is O E. The series converges because the limit used in the Ratio test is OF. The series diverges because the limit used in the Root Test is10. Does the following series converge or diverge? Give reasons for your answer. 3" nin! n = 1 (2n)! Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) A. The series diverges by the Root Test since the limit resulting from the test is The series converges by the Ratio Test since the limit resulting from the test is O B. The series diverges by the Ratio Test since the limit resulting from the test is O c. The series converges by the Root Test since the limit resulting from the test is O D. *11. Use the Root Test to determine whether the series converges. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer in terms of e.) O A. The series diverges because p = O B. The series converges because p = O C. The Root Test is inconclusive because p = *12. Use an appropriate test to determine whether the series converges. 1 8 K = 1 Select the correct answer below and fill in the answer box to complete your choice. O A. The limit of the terms of the series is , so the series diverges by the Divergence Test O B. The Ratio Test yields r = , so the series diverges by the Ratio Test. O C. The series is a geometric series with common ratio so the series converges by the properties of a geometric series. O D. The series is a geometric series with common ratio , so the series diverges by the properties of a geometric series. O E. The Ratio Test yields r = so the series converges by the Ratio Test.*13. Use the Ratio Test to determine the values of x 2 0 for which the series converges. co E 5x* 7k ! K = 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges for x (Type an exact answer in terms of e.) O C. The series converges for x = (Type an exact answer in terms of e.) O D. The series converges for all x 2 0. O E. The series diverges for all x 2 0. *14. Use the Ratio Test to determine the values of x 2 0 for which the series converges. E 4(7*)* K k = 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges for x = (Type an integer or a simplified fraction.) O B. The series converges for x > (Type an integer or a simplified fraction.) O C. The series converges for x