|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|等于多少
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![|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|等于多少](/uploads/image/z/335499-51-9.jpg?t=%7C1%2F2-1%7C%2B%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B%7C1%2F5-1%2F4%7C...%7C1%2F2011-1%2F2010%7C%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91)
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|等于多少
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|等于多少
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|等于多少
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|
=(1-1/2)+(1/2-1/3)+.+(1/2009-1/2010)+(1/2010-1/2011)
=1-1/2+1/2-1/3+.+1/2009-1/2010+1/2010-1/2011
=1-1/2011
=2010/2011
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2010-1/2011
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+……+(-1/2010+1/2010)-1/2011
=1+0+0+0+0+……+0-1/2011
=1-1/2011
=2010/2011
=-1+1/2011
=2010/2011
1/2<1 1/3<1/2 1/4<1/3 ...... 1/2001<1/2010
原式=-(1/2-1)-(1/3-1/2)-(1/4-1/3)-......-(1/2011-1/2010)
=1-1/2+1/2-1/3+1/3-1/4+......+1/2010-1/2011
=1-1/2011
=2010/2011
其实是这样的,下面去绝对值符号,有原式=1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009+1/2009-1/2010+1/2010-1/2011=1-1/2011=2010/2011(第二项加第三项为0,第四项加第五项为0……以此类推,就很容易得出结果)。