Use the ratio test to determine whether the series converges.

(a) $\displaystyle \sum_{k=1}^{\infty} \frac{3^{k}}{k!}$

Does the test reveal that the series converges, diverges or is it inconclusive. ? Converges Diverges Inconclusive

(b) $\displaystyle \sum_{k=1}^{\infty} \frac{3^{k}}{k^{2}}$

Does the test reveal that the series converges, diverges or is it inconclusive. ? Converges Diverges Inconclusive

(c) $\displaystyle \sum_{k=1}^{\infty} k\frac{1}{3^{k}}$

Does the test reveal that the series converges, diverges or is it inconclusive. ? Converges Diverges Inconclusive