Prove that \[ \frac12\cdot\frac34\cdot\frac56\cdots\frac{2n-1}{2n} \leq \frac1{\sqrt{3n}} \]

•  This is the problem that I picked up from book : 101 Solved Problem in Algebra from The USA IMO with the 43th problem.

•  As you see, this problem is related to natural number `N`, So the easiest method to solve this problem is using Mathematics Induction which you need to prove that statement is true for `n=1` , supposed that statement is true for `n=k` then the finally step is to prove It is true with `n=k+1` .
• I also translate this problem in to Khmer Language for all of you to be easy to understand both problem and solution.

• You can follow my Facebook Page: Thin Sokkean 
• Here is solution for all of you.