题型：解答题 题类：其他 难易度：较易
．已知各项均为正数的数列\(\{\)\(a_{n}\)\(\}\)的前\(n\)项和为\(S_{n}\)，满足\(a_{n+1}^{2} \)\(=\)\(2\)\(S_{n}+n+\)\(4\)，\(a\)\({\,\!}_{2}\)\(-\)\(1\)，\(a\)\({\,\!}_{3}\)，\(a\)\({\,\!}_{7}\)恰为等比数列\(\{\)\(b_{n}\)\(\}\)的前\(3\)项．
\((1)\)求数列\(\{\)\(a_{n}\)\(\}\)，\(\{\)\(b_{n}\)\(\}\)的通项公式\(;\)
\((2)\)若\(c_{n}=\)\((\)\(-\)\(1)\)\({\,\!}^{n}\)\(\log _{2}\)\(b_{n}-\)\( \dfrac{1}{{a}_{n}{a}_{n+1}} \)，求数列\(\{\)\(c_{n}\)\(\}\)的前\(n\)项和\(T_{n}\)．
