|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+.+|1/2006-1/2004|+|1/2008-1/2006|
=|1/2-1/4|+|1/4-1/4|+|1/6-1/8|+.+|1/2004-1/2006|+|1/2006-1/2008|
=1/2-1/4+1/4-1/6+1/6-1/8+……+1/2004-1/2006+1/2006-1/2008
=1/2-1/2008
=1003/2008.