\(B=\dfrac{2n-1}{n+1}\)
\(B\in N\Rightarrow2n-1⋮n+1\)
\(2n+2-3⋮n+1\)
\(2\left(n+1\right)-3⋮n+1\)
\(\Rightarrow3⋮n+1\)
\(\Rightarrow n+1\inƯ\left(3\right)\)
\(Ư\left(3\right)=\left\{\pm1;\pm3\right\}\)
\(n+1=1\Rightarrow n=0\)
khi đó:\(B=\dfrac{2.0-1}{0+1}=1\)(chọn)
\(n+1=-1\Rightarrow n=-2\)
khi đó:\(B=\dfrac{-2.2-1}{-2+1}=5\)(chọn)
\(n+1=3\Rightarrow n=2\)
khi đó: \(B=\dfrac{2.2-1}{2+1}=1\)(chọn)
\(n+1=-3\Rightarrow n=-4\)
khi đó \(B=\dfrac{-4.2-1}{-4+1}=3\)(chọn)
Vậy-