Apply the Root Test to the series ∑n=1∞(3n−14n+2)n\sum_{n=1}^{\infty} \left(\frac{3n-1}{4n+2}\right)^n∑n=1∞(4n+23n−1)n. Which statement is correct?
The series converges absolutely by the Root Test, since limn→∞∣an∣n=34<1\lim_{n \to \infty} \sqrt[n]{|a_n|} = \frac{3}{4} < 1limn→∞n∣an∣=43<1
The series diverges by the Root Test, since limn→∞∣an∣n=1\lim_{n \to \infty} \sqrt[n]{|a_n|} = 1limn→∞n∣an∣=1
The Root Test is inconclusive because the limit equals 1
The series converges conditionally by the Root Test, since limn→∞∣an∣n=43>1\lim_{n \to \infty} \sqrt[n]{|a_n|} = \frac{4}{3} > 1limn→∞n∣an∣=34>1