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 Compute limn→∞∣an+1an∣\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|limn→∞anan+1 and determine convergence.
Limit =3= 3=3; series diverges
Limit =0= 0=0; series converges
Limit =14= \frac{1}{4}=41; series converges
Limit does not exist; test is inconclusive