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.

Given
$$
(1/2)(3/4)(5/6)(7/8)\cdots([2n-1]/2n)
$$
Thus
$$
\frac{1}{2} \frac{3}{4} \frac{5}{6} \cdots \frac{2n-1}{2n} = \frac{1 \cdot 2 \cdot 3 \cdot 4 \cdots [2n-1] \cdot 2n}{2^{2n} \cdot (1 \cdot 2 \cdot 3 \cdot 4 \cdots 2n)^2 } = \frac{[2n]!}{2^n (n!)^2}
$$
