已知数列\(\left\{ {{a}_{n}} \right\}\)的首项\({{a}_{1}}=1\)，\({{S}_{n}}\)是数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和，且满足\(2\left( {{S}_{n}}+1 \right)=\left( n+3 \right){{a}_{n}}\)．

\((1)\)求数列\(\left\{ {{a}_{n}} \right\}\)的通项公式；

\((2)\)设数列\(\left\{ {{b}_{n}} \right\}\)满足\({{b}_{n}}=\dfrac{1}{{{a}_{n}}{{a}_{n+1}}}\)，记数列\(\left\{ {{b}_{n}} \right\}\)的前\(n\)项和为\({{T}_{n}}\)，求证：\({{T}_{n}} < 3\)．