Cho $I_n = \int\limits_{0}^{\frac{\pi}{2} } \sin ^n xdx, n \in N$
a) Chứng minh rằng : $\sqrt{\frac{\pi }{2(n+1)} } < I_n < \sqrt{\frac{\pi}{2n} }$
b) Từ đó suy ra rằng : $ \mathop {\lim }\limits \frac{2.4.6...(2n)}{3.5.7...(2n-1)\sqrt{2n+1} } = \frac{\pi}{2}.$