Determine whether the following series converges. Justify your answer. Summation from k equals 3 to infinity StartFraction 1 Over k Superscript four ninths Baseline ln k EndFraction Question content area bottom Part 1 Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. ​(Type an exact​ answer.) A. Let a Subscript kequalsStartFraction 1 Over k Superscript four ninths Baseline ln k EndFraction and b Subscript kequalsStartFraction 1 Over k ln k EndFraction . Since ModifyingBelow lim With k right arrow infinityStartStartFraction StartFraction 1 Over k Superscript four ninths Baseline ln k EndFraction OverOver StartFraction 1 Over k ln k EndFraction EndEndFraction equalsinfinity and Summation from k equals 3 to infinity StartFraction 1 Over k ln k EndFraction ​diverges, the series diverges by the Limit Comparison Test. B. Let a Subscript kequalsStartFraction 1 Over k Superscript four ninths Baseline ln k EndFraction and b Subscript kequalsStartFraction 1 Over k ln k EndFraction . Since ModifyingBelow lim With k right arrow infinityStartStartFraction StartFraction 1 Over k Superscript four ninths Baseline ln k EndFraction OverOver StartFraction 1 Over k ln k EndFraction EndEndFraction is nonnegative and Summation from k equals 3 to infinity StartFraction 1 Over k ln k EndFraction ​converges, the series converges by the Limit Comparison Test. C. The Ratio Test yields requals    enter your response here. This is greater than​ 1, so the series diverges by the Ratio Test. D. The terms of the series are alternating and their limit is    enter your response here​, so the series diverges by the Alternating Series Test. E. The Ratio Test yields requals    enter your response here. This is less than​ 1, so the series converges by the Ratio Test. F. The terms of the series are alternating and their limit is    enter your response here​, so the series converges by the Alternating Series Test.