求极限\[\lim_{n\to\infty}\left(\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\right)^\frac1n\]解：令\[f(n)=\left(\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\right)^\frac1n\]为了利用夹逼准则，我们先证$$\left(\frac1{2