Determine whether the following series converges. Justify your answer. 7k5 + k 5 k = 1 10k _ 1 1 (E Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) "ii? A- The series is a pseries with p = , so the series diverges by the properties of a p-series. '1":3' 3- The series is a geometric series with common ratio , so the series diverges by the properties of a geometric series. '5-3' C. The Root Test yields p = , so the series converges by the Root Test. D- The series is a p-series with p = , so the series converges by the properties of a pseries. E- The Ratio Test yields r= , so the series converges by the Ratio Test. ("3' F- The limit of the terms of the series is , so the series diverges by the Divergence Test. Determine whether the following series converges. Justify your answer. 1 k 00 1 a 4 . I I , a Is rea k = 1 (3 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) ":3? A- The series is a pseries with p = , so the series converges by the properties of a pseries. 5:33 B- The limit of the terms of the series is , so the series diverges by the Divergence Test. "'3' C- The series is a pseries with p = . so the series diverges by the properties of a pseries. 5:? D- The Ratio Test yields r= , so the series converges by the Ratio Test. "'3' E- The series is a geometric series with common ratio , so the series diverges by the properties of a geometric series. F- The series is a geometric series with common ratio , so the series converges by the properties of a geometric series. Determine whether the following series converges. Justify your answer. K 18 k = 1 18k . . . Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The series is a geometric series with common ratio , so the series diverges by the properties of a geometric series. O B. The series is a geometric series with common ratio , so the series converges by the properties of a geometric series. O C. The Root Test yields p = so the series diverges by the Root Test. O D. The Ratio Test yields r= , so the series diverges by the Ratio Test. O E. The limit of the terms of the series is , so the series diverges by the Divergence Test. OF. The Ratio Test yields r = , so the series converges by the Ratio Test.Determine whether the following series converges. Justify your answer. E) Select the correct choice below and, if necessary, ll in the answer box to complete your choice. (Type an exact answer.) :3; A. The Root Test yields p = , so the series converges by the Root Test. {:3} B. The Root Test yields p = , so the series diverges by the Root Test. 4 4k " 4 k " {f} C. Because (-1)k[] ( - 1)k[ ] ,for any positive integer k, and 2 (-1)k[] diverges. so the series diverges by the Comparison Test. 9k+7 5 k=1 {I} E. The terms of the series are alternating and their limit is , so the series diverges by the Alternating Series Test. Determine whether the following series converges. Justify your answer. E 2(3k) ! K = 1 ( K ! ) 3 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) A. The series is a geometric series with common ratio . This is greater than 1, so the series diverges by the properties of a geometric series. O B. The limit of the terms of the series is , so the series converges by the Divergence Test. O C. The Ratio Test yields r= . This is less than 1, so the series converges by the Ratio Test. O D. The Ratio Test yields r= . This is greater than 1, so the series diverges by the Ratio Test. O E. The series is a geometric series with common ratio . This is less than 1, so the series converges by the properties of a geometric series.Determine whether the following series converges. Justify your answer. 6 8 k = 1 (k+ 4)3 . . . Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The Ratio Test yields r= , so the series diverges by the Ratio Test. O B. The series is a p-series with p = , so the series converges by the properties of a p-series. 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 p-series with p = , so the series diverges by the properties of a p-series. O E. The limit of the terms of the series is , so the series diverges by the Divergence Test. OF. The series is a geometric series with common ratio , so the series diverges by the properties of a geometric series