\((1).\)双曲线的两条渐近线互相垂直,则离心率\(e=\_\_\_\_\_\).
\((2).\)观察下列等式:
\(1=1\)
\(2+3+4=9\)
\(3+4+5+6+7=25\)
\(4+5+6+7+8+9+10=49\)
照此规律第\(n\)个等式为______________________.
\((3).\)复数\(z= \dfrac{2}{1-i} \)给出四个结论:\(①\left| z \right|=2\);\(②{{z}^{2}}=2i\);\(③\overline{z}=-1+i\);\(④z的虚部为i \),正确的有__________\((\)填序号\()\)
\((4).\)若数列\(\left\{ {{a}_{n}} \right\}n\in N+\)是等差数列,则数列\({{b}_{n}}=\dfrac{{{a}_{1}}+{{a}_{2}}+\cdots {{a}_{n}}}{n}\),也是等差数列,类比上述性质,相应地有:若数列\(\left\{ {{C}_{n}} \right\}n\in N+\)是等比数列,且\({{C}_{n}} > 0\),则数列\({{d}_{n}}=\)____________也是等比数列.