\(n+1⋮2n-1\)
\(\Rightarrow2\left(n+1\right)⋮2n-1\)
\(\Rightarrow2n+2⋮2n-1\)
\(\Rightarrow2n-1+2⋮2n-1\)
\(\Rightarrow2n-1\inƯ\left(2\right)\)
\(Ư\left(2\right)=\left\{\pm1;\pm2\right\}\)
\(\Rightarrow\left\{{}\begin{matrix}2n-1=1\Rightarrow2n=2\Rightarrow n=1\\2n-1=-1\Rightarrow2n=0\Rightarrow n=0\\2n-1=2\Rightarrow2n=3\Rightarrow n=\dfrac{3}{2}\\2n-1=-2\Rightarrow2n=-1\Rightarrow n=\dfrac{-1}{2}\end{matrix}\right.\)
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