Solve the Problem $( n + 1 ) ! > 3 ^ { n }$

Multiple Choice

Solve the problem.
-Suppose you wish to prove the statement that follows using the extended principle of mathematical is $( n + 1 ) ! > 3 ^ { n }$ , for positive integers $n \geq 4$ .

Assume that $S _ { k }$ is true for $k \geq 4$ where $S _ { k }$ is the statement $( n + 1 ) ! > 3 ^ { n }$ , and write the statement $S _ { k + 1 }$

A) $S _ { k + 1 } : ( k + 2 ) ! > 3 ^ { k }$
B) $S _ { k + 1 } : ( k + 1 ) ! > 4 ^ { k }$
C) $S _ { k + 1 } : ( k + 1 ) ! > 3 ^ { k + 1 }$
D) $S _ { k + 1 } : ( k + 2 ) ! > 3 ^ { k + 1 }$ ion.