|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|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)。