Apply the root test to ∑n=1∞(4n7n+3)n\sum_{n=1}^{\infty} \left(\frac{4n}{7n+3}\right)^n∑n=1∞(7n+34n)n and determine convergence. What is limn→∞∣an∣n\lim_{n \to \infty} \sqrt[n]{|a_n|}limn→∞n∣an∣?
The limit equals 74\frac{7}{4}47 and the series diverges.
The limit equals 111 and the root test is inconclusive.
The limit equals 47\frac{4}{7}74 and the series converges.
The limit equals 000 and the series converges.