1\2*5+1\5*8+1\8*11.+1\2003*2006+1\2006*2009

1\2*5+1\5*8+1\8*11.+1\2003*2006+1\2006*2009
1\2*5+1\5*8+1\8*11.+1\2003*2006+1\2006*2009

1\2*5+1\5*8+1\8*11.+1\2003*2006+1\2006*2009
1\2*5+1\5*8+1\8*11.+1\2003*2006+1\2006*2009
=1/3(1/2-1/5+1/5-1/8+1/8-1/11+.+1/2003-1/2006+1/2006-1/2009)
=1/3(1/2-1/2009)
=2007/3*2*2009
=669/4018

1\2*5=(1\2-1\5)*1\3
1\5*8=(1\5-1\8)*1\3
.......
原式=(1\2-1\5)*1\3-(1\5-1\8)*1\3......-(1\2006-1\2009)*1\3
=(1\2-1\2009)*1\3

原式=1/3 (1/2-1/5+1/5-1/8+1/8-1/11+……+1/2003-1/2006+1/2006-1/2009)
=1/3(1/2-1/2009)
=1/3 x 2007/4018
=669/4018