f(x)=f(x-1)+f(x+1)
f(x-1)=f(x)-f(x+1)
对n为自然数,有
f(3n)=f(3n+1)-f(3n+2)=f(3n+2)-f(3n+3)-[f(3n+3)-f(3n+4)]
=f(3n+2)+f(3n+4)-2f(3n+3)=-f(3n+3)
可知:f(3n)=f(3)×(-1)^(n+1)
2007/3=669,当n=669时,有:
f(2007)=f(3)×(-1)^(669+1)=f(3)=2007
f(x)=f(x-1)+f(x+1)
f(x-1)=f(x)-f(x+1)
对n为自然数,有
f(3n)=f(3n+1)-f(3n+2)=f(3n+2)-f(3n+3)-[f(3n+3)-f(3n+4)]
=f(3n+2)+f(3n+4)-2f(3n+3)=-f(3n+3)
可知:f(3n)=f(3)×(-1)^(n+1)
2007/3=669,当n=669时,有:
f(2007)=f(3)×(-1)^(669+1)=f(3)=2007