1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2011)(b-2011)的值.(a=-2,

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/09/13 23:13:55

1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2011)(b-2011)的值.(a=-2,b=-1)

当a=-2,b=-1时
1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+……+1/(a-2011)(b-2011)
=1/[-2×(-1)]+1/[-3×(-2)]+1/[-4×(-3)]+……+1/[-2013×(-2012)]
=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2012×2013)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013
=1-1/2013
=2012/2013

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