把绝对值全部拆开,显然|1/n+1 -1/n|中前项小于后项,所以拆开后变为1/n-1/n+1
所以原式变为
1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004
=1-1/2004
=2003/2004