f(x)=f(x-1)-f(x-2)怎么证明周期为6?_数学解答

f(x)=f(x-1)-f(x-2)怎么证明周期为6?

人气：107 ℃　时间：2019-12-02 19:00:41

解答

f(x)=f(x-1)-f(x-2)
f(x-1)=f(x-2)-f(x-3)
f(x)=f(x-1)-f(x-2)=f(x-2)-f(x-3)-f(x-2)=-f(x-3)
f(x+3)=-f(x)
f(x+6)=f[(x+3)+3]=-f(x+3)=-[-f(x)]=f(x)
故f(x)周期为6