|1/3-1/2|+|1/4-1/3|+...+|1/2010-1/2009|

问题描述:

|1/3-1/2|+|1/4-1/3|+...+|1/2010-1/2009|

=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/2010
=1/2-1/2010
=(1005-1)/2010
=1004/2010
=502/1005