Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. $$\sum\limits_{n=1}^{\infty} \left(1+\frac{1}{3 n}\right)^{-n^2}$$ $L = \lim\limits_{n \to \infty} \sqrt[n]{\left| a_n \right|} =$ (Enter 'inf' for $\infty$.)

$\sum_{n=4}^{\infty} \left(1+\frac{1}{3 n}\right)^{-n^2}$ is:
A. convergent
B. divergent
C. The Root Test is inconclusive