Our teacher asked this question in a homework :
I found these pages which gave me some clues :
number theory - prove that $(2n)!/(n!)^2$ is even if $n$ is a positive integer - Mathematics
Prove that 2n choose n is less than or equal to 4^n? - Yahoo! Answers
However, I can't figure that out ! According to the 2nd page, if the right member was only , then the left member would be less than or equal to the right member.
I just don't know what to do.
You help would be appreciated.