设f(x)=sinπ/3x,求f(1)+f(2)+……+f(2011)急需啊

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设f(x)=sinπ/3x,求f(1)+f(2)+……+f(2011)急需啊设f(x)=sinπ/3x,求f(1)+f(2)+……+f(2011)急需啊设f(x)=sinπ/3x,求f(1)+f(2)

设f(x)=sinπ/3x,求f(1)+f(2)+……+f(2011)急需啊
设f(x)=sinπ/3x,求f(1)+f(2)+……+f(2011)
急需啊

设f(x)=sinπ/3x,求f(1)+f(2)+……+f(2011)急需啊
f(1)=sin(π/3)=3^0.5/2
f(2)=sin(2π/3)=3^0.5/2
f(3)=sin(3π/3)=0
f(4)=sin(4π/3)=-3^0.5/2
f(5)=sin(5π/3)=-3^0.5/2
f(6)=sin(6π/3)=sin(2π)=sin(0)=0
f(7)=sin(7π/3)=sin(2π+π/3)=sin(π/3)
……
f(1)+f(2)+f(3)+f(4)+f(5)+f(6)=0
2011/6的余数=1
f(1)+f(2)+……+f(2011)=sin(π/3)=3^0.5/2
^0.5为开平方根

2分之根号3

这种题应该前面有提示,否则是很难的!