Let $n\geq 3$ be an integer. Then the statement $(n!)^{1/n}\leq\frac{n+1}{2}$ is
a) true for every $n\geq 3$,
b) true if and only if $n\geq 5$,
c) not true for $n\geq 10$,
d) true for even integers $n\geq 6$, not true for odd $n\geq 5$.
Please help me to solve this in general method without any trial and hit method. Thanks in advance.
