Để : \(2n^2-1⋮\left(n+1\right)\)
\(\Leftrightarrow2n^2-2+1⋮n+1\)
\(\Leftrightarrow2\left(n^2-1\right)+1⋮n+1\)
\(\Leftrightarrow2\left(n-1\right)\left(n+1\right)+1⋮n+1\)
\(\Rightarrow1⋮n+1\)
\(\Rightarrow n+1\inƯ\left(1\right)\)
\(\Rightarrow n+1\in\left\{-1,1\right\}\)
\(\Leftrightarrow n\in\left\{-2,0\right\}\)
Vậy : \(n\in\left\{-2,0\right\}\)