Final answer:
The alternating series in question, ∑ₙ=2[infinity](-1)ⁿ 4/7 ln n, requires an application of the Alternating Series Test to determine convergence.
Step-by-step explanation:
To determine whether the alternating series ∑ₙ=2[∞](-1)ⁿ 4/7 ln n converges or diverges, we can use the Alternating Series Test. This test states that an alternating series ∑(-1)ⁿ a_n converges if the sequence a_n is decreasing and approaches zero. Firstly, we note that as n → ∞, ln n increases without bound, but we are considering the terms 4/7 ln n, which are positive for n > 1. Secondly, the negative sign raised to the power n ensures the terms alternate in sign. If both conditions are met, the series converges; otherwise, it diverges.