1/2/3+1/3/4+1/4/5+1/5/6+......+1/2000/2001+1/2001/2002=
1/2-1/3+1/3-1/4+1/4-1/5+1/5-。。。。+1/2001-1/2002=
1/2-1/2002=1000/2002=500/1001
1/2/3+1/3/4+1/4/5+1/5/6+......+1/2000/2001+1/2001/2002=
1/2-1/3+1/3-1/4+1/4-1/5+1/5-。。。。+1/2001-1/2002=
1/2-1/2002=1000/2002=500/1001