`A=(1+1/1.3)(1+1/2.4)(1+1/3.5)...(1+1/{n(n+2)})`
`⇒A={1.3+1}/1.3.{2.4+1}/2.4.{3.5+1}/3.5...{n(n+2)+1}/{n(n+2)}`
`⇒A=2^2/1.3. 3^3/2.4. 4^4/3.5...{(n+1)^2}/{n(n+2)}`
`⇒A={2.2.3.3.4.4...(n+1)(n+1)}/{1.3.2.4.3.5...n(n+2)}`
`⇒A={2n+2}/{n+2}`
Khi `n≥1⇒`$\begin{cases}2n+2≥4\\n+2≥3\end{cases}$
`⇒A≤4/3`
`⇒A<2` `(đpcm)`