1/2011×2012×(1×2+2×3+3×4+...+2011×2012)的简便计算大神们帮帮忙

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1/2011×2012×(1×2+2×3+3×4+...+2011×2012)的简便计算大神们帮帮忙
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1/2011×2012×(1×2+2×3+3×4+...+2011×2012)的简便计算大神们帮帮忙
1/2011×2012×(1×2+2×3+3×4+...+2011×2012)的简便计算大神们帮帮忙

1/2011×2012×(1×2+2×3+3×4+...+2011×2012)的简便计算大神们帮帮忙
1/(2011x2012)x(1x2+2x3+3x4+……+2011x2012) =1/(2011x2012)x[(1+2+3+……+2011)+(1+2+3+……+2011)] =1/2011x2012x[2011x(2011+1)(2x2011+1)/6+2011x(1+2011)/2] =1/2012x(2012x4023/6+2012/2) =4023/6+1/2 =1341/2+1/2 =671
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