已知函数f（x）=sin^π/4x-√3sinπ/4xcosπ/4x 1.求f x的最大值及此时X的值2.求F(1)+F(2)+F(3)+..+F(2011)的值
解析：∵函数f（x）=sin^π/4x-√3sinπ/4xcosπ/4x=1/2-sin(π/2x+π/6)
π/2x+π/6=2kπ-π/2==>π/2x=2kπ-2π/3==>x=4k-4/3（k为整数）
f(-4/3)=1/2-sin(-2π/3+π/6)=3/2
∴当x=4k-4/3（k为整数）时,f(x)取最大值3/2
F(1)+F(2)+F(3)+F(4)=4*1/2-(sin(4π/6)+sin(7π/6)+sin(10π/6)+sin(13π/6))=2-(√3/2-1/2-√3/2+1/2)=2
F(1)+F(2)+F(3)+..+F(2011)=502*2+F(2009)+F(2010)+F(2011)=1004+3/2-1/2=1005