Apply the Ratio Test to ∑n=1∞n!⋅3n(2n)!\sum_{n=1}^{\infty} \frac{n! \cdot 3^n}{(2n)!}∑n=1∞(2n)!n!⋅3n. What is the limit and what does it imply?
The limit is 0, so the series converges
The limit is 1, so the Ratio Test is inconclusive
The limit is 32\frac{3}{2}23, so the series diverges
The limit is ∞\infty∞, so the series diverges