$\lim_{n \rightarrow \infty} ( 1 - \frac{2}{2.3}) ( 1 - \frac{2}{3.4}).......(1-\frac{2}{(n+1).(n+2)})$ Evaluate  
$\lim_{n \rightarrow  \infty} \left( 1 - \frac{2}{2\cdot3}\right) \left( 1 - \frac{2}{3\cdot4}\right)\ldots\left( 1 - \frac{2}{(n+1)(n+2)}\right)$
My attempts : i know  that  $1 -   \frac {2}{k(k+1)} = \frac{(k+2)(k-1)}{k(k+1)}$
After that I'm not able to proceed  further.
Any hints/solution will be apprecaited.
Thanks you and thanks in advance.

Hint: 
\begin{eqnarray*}
\frac{ 1\times 4}{ 3\times 2}\times \frac{ 2\times 5}{ 4\times 3}\times \frac{ 3 \times 6}{ 5 \times 4}\times \cdots 
\end{eqnarray*}
