\((1)\)因式分解:\({a}^{2}−4{b}^{2}+4b−1= \) .
\((2)\)某一程序运行如图所示,规定:从“输入一个值\(x \)”到“结果是否\( > 100 \)”为一次程序操作,如果程序操作进行了三次才停止,那么\(x \)的取值范围是 .
\((3)\)如图,在\(x \)轴的正半轴上依次截取\(O{A}_{1}={A}_{1}{A}_{2}={A}_{2}{A}_{3}=⋯={A}_{n−1}{A}_{n} \),过点\(A_{1}\),\(A_{2}\),\(A_{3}……A_{n}\)分别作\(x \)轴的垂线与反比例函数\(y= \dfrac{4}{x}(x > 0) \)的图象相交于点\(P_{1,}P_{2,}P_{3,}……\),\(Pn\),得直角三角形\(OP_{1}A_{1}\),\(A_{1}P_{2}A_{3}\),\(A_{2}P_{3}A_{3}\),\(……\),\(A_{n-1}PnA_{n}\)并设其面积分别为\(S_{1}\),\(S_{2}\),\(S_{3}……Sn\)则\({S}_{n} \)的值为 .
\((4)\)在\(\triangle \)\(ABC\)中,\(∠\)\(ACB=\)\(90^{\circ}\),\(AB=\)\(5\),\(BC=\)\(3.\)\(P\)是\(AB\)边上的动点\((\)不与点\(B\)重合\()\),将\(\triangle \)\(BCP\)沿\(CP\)所在的直线翻折,得到\(\triangle \)\(B′CP\),连接\(B′A\).
有下列说法:
\(①\)当\(AP=BP\)时,\(AB′\)\(/\!/\)\(CP\);
\(②\)当\(AP=BP\)时,\(∠B′PC=2∠B′AC\);
\(③\)当\(CP⊥AB\)时,\(AP= \dfrac{17}{5} \);
\(④B′A\)长度的最小值是\(1\).
其中说法正确的有 \(.(\)把所有正确结论的序号都选上\()\)