解方程,1×2/x+2×3/x+3×4/x+4+5 - 知识问答

解方程,1×2/x+2×3/x+3×4/x+4+5/x+……+2007+2008/x=2007

1个回答

1×2/x+2×3/x+3×4/x+4×5/x+……+2007×2008/x
=x(1-1/2)+x(1/2-1/3)+x(1/3-1/4)+.+x(1/2007-1/2008)
=x(1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008)
=x(1-1/2008)
=2007x/2008
=2007
所以x=2008

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