Finding limit of a sequence in product form \begin{equation} \prod_{n=2}^{\infty} \left (1-\frac{2}{n(n+1)}  \right )^2 \end{equation}
I need to find limit for the following product..answer is $\frac{1}{9}$.
I have tried cancelling out but can't figure out.
Its a monotonically decreasing sequence so will converge to its infimum..
how to find the infimum?

The product is equal to $\left(\frac{2-1}{2+1}\frac{n+2}{n}\right)^2$
and the limit is 1/9.
