This homework problem has me stumped.

Show that C(n,floor(n/2)) ≥ (2^n)/n

C(n,r) means the number of r-combinations, i.e.,

                n!
C(n,r) = --------
             r!(n-r)!

It says to use corollary 1 from the book, which is:

n
∑     C(n,k) = 2^n
k=0

Thanks in advance.