1/2×1/3+1/3×1/4+1/4×1/5+...+1/2001×2002+1/2002×2003 =(1/2-1/3+1/3-1/4+1/4-1/5+...+1/2001-1/2002+1/2002-1/2003 =1/2-1/2003 =2001/4006
