求 2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010 的值
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求2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010的值求2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010的值求2/1×2+2
求 2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010 的值
求 2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010 的值
求 2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010 的值
利用列项求和
2/1×2+2/2×3+2/3×4+…+2/2008×2009+2/2009×2010
=2(1-1/2)+2(1/2-1/3)+2(1/3-1/4)+...+2(1/2008-1/2009)+2(1/2009-1/2010)
=2(1-1/2+1/2-1/3+...+1/2009-1/2010)
=2(1-1/2010)
=2*2009/2010
=2009/1005