Product in terms of $n$ of $\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot \cdots \cdot \frac{2n-1}{2n}$ What is the following product in terms of $n$?
$$\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot \cdots \cdot \frac{2n-1}{2n}$$
Thank you.

$$\frac{1}{2}\frac{3}{4}\frac{5}{6} \dotsb \frac{2n-1}{2n}=\frac{1\mathbf{2}3\mathbf{4}5 \dotsb (2n-1)\mathbf{2n}}{(2 \cdot 4 \cdot 6 \dotsb 2n)^2}=\frac{(2n)!}{2^{2n}(n!)^2}$$
