|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011|计算

|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011|计算
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011|计算

|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011|计算
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011|
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2011-1/2012
=1-1/2012
=2011/2012

嗯，
|1/2-1|=1-1/2,
|1/3-1/2|=1/2-1/3，
以此类推，
|1/2012-1/2011|=1/2011-1/2012
所以原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.。。。。。。。+1/2010-1/2011+1/2011-2012
中间全部抵消，剩下1-1/2012=2011/2012