1/2*1/3=1/2-1/3
1/3*1/4=1/3-1/4
.
1/2003*1/2004=1/2003-1/2004
故原式=1/2+1/2-1/3+1/3-1/4+1/4-1/5...+1/2003-1/2004=1-1/2004=2003/2004