若函数fx=cosπx/3,（x属于整数）则f(0)+f(1)+f(2)+.f（2009）=
问题描述：
若函数fx=cosπx/3,（x属于整数）则f(0)+f(1)+f(2)+.f（2009）=
答
∵f(x)=cos(xπ/3)∴f(0)=1f(1)=cosπ/3=1/2f(2)=cos2π/3=cos(π/2-π/6)=-sin(π/6)=-1/2f(3)=cosπ=-1f(4)=cos(4π/3)=cos(π+π/3)=-cosπ/3=-1/2f(5)=cos5π/3=cos(2π-π/3)=cosπ/3=1/2……f(2009)=cos2009π...