已知数列\( \dfrac {8\cdot 1}{1^{2}\cdot 3^{2}},\;\; \dfrac {8\cdot 2}{3^{2}\cdot 5^{2}},\;…,\; \dfrac {8n}{(2n-1)^{2}(2n+1)^{2}},\;…. S _{n}\)为其前\(n\)项和．计算得\(S_{1}= \dfrac {8}{9},\;\;S_{2}= \dfrac {24}{25},\;\;S_{3}= \dfrac {48}{49},\;\;S_{4}= \dfrac {80}{81}.\)观察上述结果，推测出计算\(S _{n}\)的公式，并用数学归纳法加以证明．