已知数列\(\{a_{n}\}\)满足\(n{a}_{n}-\left(n+1\right){a}_{n-1}=2{n}^{2}+2n(n=2,3,4...),{a}_{1}=6 \)
\((1)\)求证\(\left\{ \dfrac{{a}_{n}}{n+1}\right\} \)为等差数列，并求出\(\{a\)\(n\)\(\}\)的通项公式
\((2)\)数列\(\left\{ \dfrac{1}{{a}_{n}}\right\} \)的前\(n\)项和\(S_{n,}\)求求证：\({S}_{n} < \dfrac{5}{12} \)