拆项法
1/1*3+1/3*5+1/5*7+……+1/2003*2005
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.+1/2(1/2003-1/2005)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.+1/2003-1/2005)
=1/2(1-1/2005)
=1/2×2004/2005
=1002/2005