若f(x)=sin(πx/3),则f(1)+f(2)+f(3)+……+f(2010)=?

题目

若f(x)=sin(πx/3),则f(1)+f(2)+f(3)+……+f(2010)=?

答案

f(x)=sin(πx/3)的周期是2π/（π/3）=6,f(x) = - f(-x)f(1)= - f(-1 + 6)= - f(5)f(2)= - f(-2 + 6)= - f(4)f(3)= f(6)=0=> f(1)+f(2) +f(3)+ f(4)+ f(5)+ f(6)=0f(1)+...f(2010)=335 *[ f(1)+f(2) +f(3)+ f(4)+ f(...