|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+.+|1/2010-1/2009|=?请详细的回答下．谢谢～

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+.+|1/2010-1/2009|=?请详细的回答下．谢谢～
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+.+|1/2010-1/2009|=?请详细的回答下．谢谢～

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+.+|1/2010-1/2009|=?请详细的回答下．谢谢～
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+.+|1/2010-1/2009|
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6.+1/2009-1/2010
=1/2-1/2010
=502/1005

原式=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6......+1/2009-1/2010=1/2-1/2010=502/1005