Assume that $| \frac{a_{n+1}}{a_n}|$ converges to $\rho = \frac{1}{3}$. What can you say about the convergence of the given series? $$\sum\limits_{n=1}^{\infty} {b_n} = \sum\limits_{n=1}^{\infty} a_n^2$$ $\lim\limits_{n \to \infty} \left| \frac{b_{n+1}}{b_n} \right| =$ (Enter 'inf' for $\infty$.)

$\sum\limits_{n=1}^{\infty} a_n^2$ is:
A. convergent
B. divergent
C. The Ratio Test is inconclusive