观察下列等式:1乘2分之1=1-2分之11/1×2+1/2×3+1/3×4+…+1/2009×2010

问题描述:

观察下列等式:1乘2分之1=1-2分之1
1/1×2+1/2×3+1/3×4+…+1/2009×2010

1/1×2+1/2×3+1/3×4+…+1/2009×2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010