Question

[Huy Cao]

1. \(\sin^3\frac{x}{3}+3\sin^3\frac{x}{3^2}+...+3^{n-1}\sin^3\frac{x}{3}=\frac{1}{4}\left(3^n\sin^3\frac{x}{3^n}-\sin x\right)\)
2. \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{2n+1}{2n+2}<\frac{1}{\sqrt{3n+4}}\left(n\ge1\right)\)
3. \(\left(n!\right)^2\ge n^2\ge\left(n+1\right)^{n-1}cho\left(n\ge1\right)\)