|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+……+|1/2011-1/2010|的值为?

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+……+|1/2011-1/2010|的值为?
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+……+|1/2011-1/2010|的值为?

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+……+|1/2011-1/2010|的值为?
原式=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2009-1/2010)+(1/2010-1/2011)
=1/2-1/2011
=2009/4022

绝对值中都是负数，去绝对值得：
1/2-1/3+1/3-1/4+1/4-1/5+…+1/2010-1/2011=1/2-1/2011=2009/4022