a=1 b=2
原式=1/(1*2)+1/(2*3)+1/(2006*2007)
如果要求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2005)(b+2005)
则=1-1/2+1/2-1/3+……+1/2006-1/2007=1-1/2007=2006/2007