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Determine whether the following series converges. Justify your answer. K =3 k In kSelect the correct choice below and, if necessary, fill in the answer box to complete your choice (Type an exact answer.) O A. The terms of the series are alternating and their limit is so the series converges by the Alternating Series Test In k 00 O B. Let ak 1 and bk = k Ink Since lim is nonnegative and 1 k Ink converges, the series converges by the Limit Comparison Test K -+ 0o K = 3 K Ink kInk 1 1 1 k Ink O C. Let ak = 1 and bk = k Ink Since lim = co and M diverges, the series diverges by the Limit Comparison Test. K-+0o 1 k Ink K = 3 K Ink k In k O D. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test. O E. The Ratio Test yields r = This is less than 1, so the series converges by the Ratio Test.O A. The terms of the series are alternating and their limit is , so the series converges by the Alternating Series Test GILD In k 1 O B. K Let ak = and bk = k Ink Since lim is nonnegative and M kInk converges, the series converges by the Limit Comparison Test. 1 K-+00 K = 3 K In k k Ink 1 K Ink 0O 1 O C. Let ak and bk = Since lim = co and diverges, the series diverges by the Limit Comparison Test. k Ink K- OO 1 k Ink K =3 k Ink k Ink OD. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test. O E. The Ratio Test yields r = This is less than 1, so the series converges by the Ratio Test. OF. The terms of the series are alternating and their limit is , so the series diverges by the Alternating Series Test