先去绝对值,再把中间项消去即可.
原式=1/2007-1/2008+1/2006-1/2007+1/2005-1/2006+1/2004- 1/2005+.+1/4-1/5+1/3-1/4+1/2-1/3
=1/2-1/2008=1003/2008