For each of the following, carefully determine whether the series converges or not.

(a) $\sum\limits_{n=1}^{\infty}\,{(n-1)!\over n^3}$
A. converges
B. diverges

(b) $\sum\limits_{n=1}^{\infty}\,{(-1)^{n-1} n^3\over 4^n}$
A. converges
B. diverges

(c) $\sum\limits_{n=2}^{\infty}\,{4\over\ln n^3}$
A. converges
B. diverges

(d) $\sum\limits_{n=4}^{\infty}\,{\sqrt{n^2 - 4}\over n^3 - 3 n}$
A. converges
B. diverges