Use the Ratio Test to analyze ∑n=1∞n!⋅2n32n\sum_{n=1}^{\infty} \frac{n! \cdot 2^n}{3^{2n}}∑n=1∞32nn!⋅2n. What is the result?
Converges; ρ=0\rho = 0ρ=0
Diverges; ρ=∞\rho = \inftyρ=∞
Converges; ρ=23\rho = \frac{2}{3}ρ=32
Test is inconclusive; ρ=1\rho = 1ρ=1