Apply the Ratio Test to ∑n=1∞n3⋅3n5n⋅n!\sum_{n=1}^{\infty} \frac{n^3 \cdot 3^n}{5^n \cdot n!}∑n=1∞5n⋅n!n3⋅3n. What is limn→∞∣an+1an∣\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|limn→∞anan+1?
limn→∞∣an+1an∣=0\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = 0limn→∞anan+1=0; series converges
limn→∞∣an+1an∣=35\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = \frac{3}{5}limn→∞anan+1=53; series converges
limn→∞∣an+1an∣=1\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = 1limn→∞anan+1=1; test is inconclusive
limn→∞∣an+1an∣=53\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = \frac{5}{3}limn→∞anan+1=35; series diverges