Ta có: \(a\left(a+2\right)< a\left(a+2\right)+1=a^2+2a+1=\left(a+1\right)^2\)
\(\Rightarrow a\left(a+2\right)< \left(a+1\right)^2\)
Ta có : \(a\left(a+2\right)< a\left(a+2\right)+1=a^2+2a+1=\left(a+1\right)^2\)
\(\Rightarrow\) \(a\left(a+2\right)< \left(a+1\right)^2\)
\(\Rightarrow\) đpcm