数列\(\{a _{n} \}\)满足\(a_{1}=1,a_{2}=3\text{且} \dfrac {a_{n+2}}{a_{n+2}-a_{n+1}}= \dfrac {2a_{n+1}-a_{n}}{a_{n+1}-a_{n}}(n∈N^{*})\)．
\((1)\)设\(b_{n}= \dfrac {a_{n}}{a_{n+1}-a_{n}}\)，证明：数列\(\{b _{n} \}\)是等差数列；
\((2)\)设\(c_{n}= \dfrac {(a_{n}+1)^{2}}{a_{n}a_{n+1}}\)，求数列\(\{c _{n} \}\)的前\(n\)项和为\(S _{n}\)．