Apply the root test to ∑n=1∞(n3n+2)n\sum_{n=1}^{\infty} \left(\frac{n}{3n+2}\right)^n∑n=1∞(3n+2n)n. What is limn→∞∣an∣n\lim_{n \to \infty} \sqrt[n]{|a_n|}limn→∞n∣an∣ and what does it tell us?
13\frac{1}{3}31; the series converges
111; the root test is inconclusive
333; the series diverges
000; we need another test to determine convergence