若x0满足方程f(x0)=x0,则称x0是函数f(x)的一个不动点,利用不动点可将某些由递推关系所确定的数列转化为等差、等比数列.下面举例说明.结论1若f(x)=ax+b(a≠0,a≠1),x0为f(x)的不动点,{an}满足an=f(an-1)(n≥2),则{an-x0}是公比为a的等比数列.证明因为x0为f(x)的不动点,所以ax0 If x0 satisfies the equation f (x0) = x0, then x0 is a fixed point of the function f (x). Using the fixed point, some sequences determined by the recursion relation can be transformed into an equal-difference sequence The following is an example: CONCLUSION 1 If x (x) is the fixed point of f (x) and f (x) = ax + b (a ≠ 0, a ≠ 1) n ≧ 2), then {an-x0} is a geometric sequence with a common metric a. Prove that because x0 is the fixed point of f (x), ax0