1/1*2*3+1/2*3*4.1/2005*2006*2007
=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+.+1/2*(1/2005*2006-1/2006*2007)
=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+/2005*2006-1/2006*2007)
=1/2*(1/2-1/2006*2007)
=1/2*2013020/2006*2007
=1006510/(2006*2007)
=503255/2019042
晕啊,算的累死我了!
您只要知道技巧就可以了~