Induction: Show: $\frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times ... \times \frac{2n-1}{2n} \leq \frac{1}{\sqrt{3n+1}}$
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$