1/1×2+1/2×3+1/3×4+……+1/20 - 知识问答

1/1×2+1/2×3+1/3×4+……+1/2005×2006+1/2006×2007+1/2007×2008

3个回答

1/1×2+1/2×3+1/3×4+……+1/2005×2006+1/2006×2007+1/2007×2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2005-1/2006)+(1/2006-1/2007)+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006+1/2006-1/2007+1/2007-1/2008
中间抵消
=1-1/2008
=2007/2008

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