(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+(-1/4*1/5)+""+(-1/2005*1/2006

原式=(-1)×[1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(2005×2006)+1/(2006×2007)]
=(-1)×[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2005-1/2006)+(1/2006-1/2007)]
=(-1)×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2005-1/2006+1/2006-1/2007)
=(-1)×(1-1/2007)
=(-1)×2006/2007
= -2006/2007

1*2/1 2*3/1 3*4/1 4*5/1. 2006*2007/1 =1-1/2 1/2-1/3 1/3-1/4 1/4-1/5 …… 1/2006-1/2007 =1-1/2007 =2006/2007 .

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