Converges, with $\lim_{n \to \infty} \sqrt[n]{a_n} = \frac{3}{7} < 1$

Diverges, with $\lim_{n \to \infty} \sqrt[n]{a_n} = \frac{3}{7}$

Converges, with $\lim_{n \to \infty} \sqrt[n]{a_n} = 1$

The Root Test is inconclusive for this series