10.
已知数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),对一切正整数\(n\),点\(P_{n}(n,S_{n})\)都在函数\(f(x)=x^{2}+2x\)的图像上,且过点\(P_{n}(n,S_{n})\)的切线的斜率为\(k_{n}\).
\((\)Ⅰ\()\)求数列\(\{a_{n}\}\)的通项公式;
\((\)Ⅱ\()\)若\({b}_{n}= \dfrac{1}{{a}_{n}·({k}_{n}+1)} \),求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}\).