Use any method $($comparison test, ratio test or root test$)$ to determine whether the series converges.

a$){\displaystyle \underset{k=1}{\overset{}{}}}\frac{\sqrt[\phantom{2}]{k}}{k^3+1}$

b$){\displaystyle \underset{k=1}{\overset{}{}}}\frac{k!}{k^k}$