Final answer:
The given alternating series converges according to the Alternating Series Test since the absolute values of the terms decrease monotonically to zero.
Step-by-step explanation:
The question involves determining the convergence or divergence of the given alternating series ∑ₙ=1[infinity](-1)ⁿ+1²2ⁿ/ₙ². To determine convergence, we use the Alternating Series Test, which states that an alternating series converges if the absolute values of the terms decrease monotonically to zero. In this case, the nth term of the series is given by aₙ = 2ⁿ/ₙ². As n goes to infinity, aₙ goes to zero, and since 2ⁿ/ₙ³ decreases monotonically, the series satisfies both conditions of the Alternating Series Test and thus converges.