1/1+2+1/1+2+3+1/1+2+3+4.1/1+2+3.2011
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![1/1+2+1/1+2+3+1/1+2+3+4.1/1+2+3.2011](/uploads/image/z/6749437-13-7.jpg?t=1%2F1%2B2%2B1%2F1%2B2%2B3%2B1%2F1%2B2%2B3%2B4.1%2F1%2B2%2B3.2011)
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1/1+2+1/1+2+3+1/1+2+3+4.1/1+2+3.2011
1/1+2+1/1+2+3+1/1+2+3+4.1/1+2+3.2011
1/1+2+1/1+2+3+1/1+2+3+4.1/1+2+3.2011
1/1+2+1/1+2+3+1/1+2+3+4.1/1+2+3.2011
=2*【1/6+1/12+1/20+……+1/(2011×2012)】
=2*【1/2-1/3+1/3-1/4+1/4-1/5+……+1/2011-1/2012】
=2*【1/2-1/2012】
=1-1/1006
=1005/1006