Apply the Ratio Test to ∑n=1∞n2⋅4n(n+1)!\sum_{n=1}^{\infty} \frac{n^2 \cdot 4^n}{(n+1)!}∑n=1∞(n+1)!n2⋅4n. What is limn→∞∣an+1an∣\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|limn→∞anan+1, and what does the test conclude?
The limit is 0, so the series converges
The limit is 4, so the series diverges
The limit is 1, so the test is inconclusive
The limit is 4e\frac{4}{e}e4, so the series diverges