Determine the convergence of the series ∑n=1∞(n!)23n(2n)!\sum_{n=1}^{\infty} \frac{(n!)^2}{3^n (2n)!}∑n=1∞3n(2n)!(n!)2.
Converges by the Ratio Test (L=1/4L = 1/4L=1/4)
Converges by the Ratio Test (L=1/12L = 1/12L=1/12)
Diverges by the Ratio Test
Inconclusive by the Ratio Test