For Which Positive Integers $k$ Is the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 5 } } { ( k n ) ! }$

Multiple Choice

For which positive integers $k$ is the series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 5 } } { ( k n ) ! }$ convergent? Select the correct answer.

A) $k \geq 5$
B) $k \leq 0$
C) $k \geq 0$
D) $k \geq 1$
E) $k \leq - 5$