已知数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)满足\(S_{n}-n=2a_{n}.\)
\((1)\)求\(\{a_{n}\}\)的通项公式；
\((2)\)若\(b_{n}=\dfrac{n+1}{a_{n+1}-1}\)，数列\(\{b_{n}\}\)的前\(n\)项和为\(T_{n}\)，求证：\(-\dfrac{3}{2}< T_{n}\leqslant-\dfrac{1}{2}.\)