|1/3-1/2|+|1/4-1/3|+...=(1/2-1/3)+(1/3-1/4)+...+(1/2009-1/2010)
=1/2-(1/3-1/3)-(1/4-1/4)-...-(1/2009-1/2009)-1/2010
=1/2-1/2010
=502/1005
绝对值内全为负,可去掉.