Provide an Appropriate Response $\sqrt [ n ] { n ! } \approx \frac { n } { e }$

Multiple Choice

Provide an appropriate response.
-It can be shown that $\sqrt [ n ] { n ! } \approx \frac { n } { e }$ for large values of $n$ . Find the smallest value of $N$ such that $\frac { \sqrt [ n ] { n ! } } { \frac { n } { e } } - 1 < 10 ^ { - 1 }$ for all $\mathrm { n } > \mathrm { N }$ .

A) 29
B) 33
C) 27
D) 22