1×2分之x+2×3分之x+...+2010×2011分之x=2010(1-1/2)x+(1/2-1/3)x+……+(1/2010-1/2011)x=2010x-1/2x+1/2x-1/3x+……+1/2010x-1/2011x=2010x-1/2011x=20102010/2011x=2010x=2010÷2010/2011x=2011