观察1/2X3=1/2-1/3 1/3X4=1/3-1/4 1/4X5=1/4-1/5计算1/6+1/12+1/20+1/30+…+1/2005X2006
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![观察1/2X3=1/2-1/3 1/3X4=1/3-1/4 1/4X5=1/4-1/5计算1/6+1/12+1/20+1/30+…+1/2005X2006](/uploads/image/z/13871786-50-6.jpg?t=%E8%A7%82%E5%AF%9F1%2F2X3%3D1%2F2-1%2F3+1%2F3X4%3D1%2F3-1%2F4+1%2F4X5%3D1%2F4-1%2F5%E8%AE%A1%E7%AE%971%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B%E2%80%A6%2B1%2F2005X2006)
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观察1/2X3=1/2-1/3 1/3X4=1/3-1/4 1/4X5=1/4-1/5计算1/6+1/12+1/20+1/30+…+1/2005X2006
观察1/2X3=1/2-1/3 1/3X4=1/3-1/4 1/4X5=1/4-1/5
计算1/6+1/12+1/20+1/30+…+1/2005X2006
观察1/2X3=1/2-1/3 1/3X4=1/3-1/4 1/4X5=1/4-1/5计算1/6+1/12+1/20+1/30+…+1/2005X2006
1/6+1/12+1/20+1/30+…+1/2005X2006
=1/2x3+1/3x4+1/4x5+1/5x6+……+1/2005X2006
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2005-1/2006
=1/2-1/2006
=501/1003