如图，点列\(\{A_{n}\}\)，\(\{B_{n}\}\)分别
在某锐角的两边上，且\(\left| {{A}_{n}}{{A}_{n+1}} \right|=\left| {{A}_{n+1}}{{A}_{n+2}} \right|,{{A}_{n}}\ne {{A}_{n+2}},n\in {{N}^{*}}\)，\(\left| {{B}_{n}}{{B}_{n+1}} \right|=\left| {{B}_{n+1}}{{B}_{n+2}} \right|,{{B}_{n}}\ne {{B}_{n+2}},n\in {{N}^{*}}\)，\((P\neq Q \)表示点\(P\)与\(Q\)不重合\()\)，若\({d}_{n}=\left|{A}_{n}{B}_{n}\right| \) \(S_{n}\)为\(∆{A}_{n}{B}_{n}{B}_{n+1} \)的面积，则\((\) \()\)
