Limit problem involving a double factorial

[powerof]

Homework Statement

Solve the following limit:
$$ \lim_{n\rightarrow \infty }n\cdot\left ( \frac{2\cdot4\cdot6 \cdots (2n-2)}{1\cdot3\cdot5\cdots (2n-1)} \right )^{2}$$

The Attempt at a Solution

I don't know where to begin. Until know I've encountered limits which I could deal with in some way but this is new for me. Any tips?

Thank you for your time.

 

[haruspex]

Consider the ratio of two consecutive terms.