1x1\3=1/2*(1/1-1/3)2x1\4=1/2*(1/2-1/4).1x1\3+2x1\4+3x1\5+.+2006x1\2008=1/2(1/1-1/3+1/2-1/4+1/3-1/5+.+1/2005-1/2007+1/2006-1/2008)=1/2(1+1/2-1/2007-1/2008)=6041069/8060112