已知函数f(n)-sinnπ/3(n属于Z)

f(n)=sin(nπ/3)(n属于Z) T=2π/(π/3)=6 一个周期内的和是： f(1)+f(2)+f(3)+f(4)+f(5)+f(6) =sin(π/3)+sin(2π/3)+sin(π)+sin(4π/3)+sin(5π/3)+sin(2π) =√3/2+√3/2+0-√3/2-√3/2+0 =0 而200=33×6+2 所以f(1)+f(2)+...+f(200) =f(1