已知数列\(\{a _{n} \}\)是首项为\(1\)的等差数列，数列\(\{b _{n} \}\)是公比不为\(1\)的等比数列，且满足\(a _{1} +a _{2} =b _{2}\)，\(a _{2} +a _{3} =b _{3}\)，\(a _{4} +a _{5} =b _{4}\)．
\((1)\)求数列\(\{a _{n} \}\)，\(\{b _{n} \}\)的通项公式；
\((2)\)令\(c_{n}= \dfrac {a_{n+2}b_{n+2}}{(a_{n}b_{n}+1)(a_{n+1}b_{n+1}+1)}(n∈N^{*})\)，记数列\(\{c _{n} \}\)的前\(n\)项和为\(S _{n}\)，求证：对任意的\(n∈N*\)，都有\(1 < S_{n} < \dfrac {4}{3}\)；
\((3)\)若数列\(\{d _{n} \}\)满足\(d _{1} =1\)，\(d _{n} +d _{n+1} =b _{n}\)，记\(T_{n}= \sum\limits_{k=1}^{n} \dfrac {d_{k}}{b_{2k}}\)，是否存在整数\(λ\)，使得对任意的\(n∈N*\)都有\(1\leqslant λT_{n}- \dfrac {d_{n}}{b_{2n}} < 2\)成立？若存在，求出\(λ\)的值；若不存在，说明理由．