For Which Positive Integers K Is the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 4 } } { ( k n ! ) }$

For which positive integers k is the series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 4 } } { ( k n ! ) }$ convergent?

A) $k \geq 4$
B) $k \leq - 4$
C) $k \leq 0$
D) $k \geq 0$
E) $k \geq 1$