已知f(n)=sin (nx/3),f(1)+f(2)+.........+f(2010)=

f(x) 周期为 6 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 = sin π/3 + sin 2π/3 + 0 + sin -2π/3 + sin -π/3 + 0 = sin π/3 + sin 2π/3 + 0 - sin 2π/3 - sin π