【数学函数问题】已知:f(x)=sin[π/3(x+1)]-根号3cos[π/3(x+1)],则f(1)+f(2)+f(

f(x)=2(sin[π/3(x+1)]/2-√3/2cos[π/3(x+1)])=2(sin[π/3(x+1)]cosπ/3-sinπ/3cos[π/3(x+1)])
=2sin(π/3x)
f(1)+f(2)+f(3)+f(4)+f(5)+f(6)=0
f(1)+f(2)+f(3)+f(4)+f(5).+f(2009)=f(1)+f(2)+f(3)+f(4)+f(5)=0