已知数列an满足a1=0,an+1=an-根号3/根号3an+1,则a2012=

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已知数列an满足a1=0,an+1=an-根号3/根号3an+1,则a2012=已知数列an满足a1=0,an+1=an-根号3/根号3an+1,则a2012=已知数列an满足a1=0,an+1=an

已知数列an满足a1=0,an+1=an-根号3/根号3an+1,则a2012=
已知数列an满足a1=0,an+1=an-根号3/根号3an+1,则a2012=

已知数列an满足a1=0,an+1=an-根号3/根号3an+1,则a2012=
a1=0,
a2=(a1-√3)/(√3a1+1)=-√3
a3=(a2-√3)/(√3a2+1)=-2√3/(-2)=√3
a4=(a3-√3)/(√3a3+1)=(√3-√3)/4=0
……
规律:从a1开始,按0,-√3,√3循环,每3个循环一次.
2010/3=670,正好循环670次.
a2010=√3