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x^2-px-q=0
a_n=a_1\sum_{k=0}^{n-1}\alpha^{n-1}-\alpha^2a_0\sum_{k=0}^{n-2}\alpha^{n-2}=na_1\alpha^{n-1}-(n-1)a_0\alpha^n
a_{n+2}-\alpha a_{n+1}=\alpha(a_{n+1}-\alpha a_n)=\alpha^{n+1}(a_1-\alpha a_0)
a_{n+1}-\frac{1}{2}=-(a_n-\frac{1}{2})=(-1)^{n}(a_1-\frac{1}{2})=\frac{(-1)^{n}}{2}
a_n=a_0p^n+\alpha(1-p^n)=a_0p^n+q\sum_{k=0}^{n-1}p^k;\ \ n=1,\ 1-p=0