学帮网对所有非负整数都有f(x)=f(x-1)+f(x+1)且f(0)=2004`求f(2004)
来源：学生作业学帮网 编辑：学帮网 时间：2024/06/06 06:08:41
对所有非负整数都有f(x)=f(x-1)+f(x+1)且f(0)=2004`求f(2004)
f(x+1) = f(x) - f(x-1)
f(x+2) = f(x+1) - f(x) = f(x) - f(x-1) - f(x) = -f(x-1)
可替换为
f(x) = - f(x-3) = f(x-6)
f(2004) = f(1998) = f(1992) = ……
2004/6 = 334
因此 f(2004) = f(0) = 2004