1.1/2+1/2*3+1/3*4+…+1/2006*2007
=1-1/2+1/2-1/3+1/3-1/4+……+1/2006-1/2007
=1-1/2007=2006/2007
2.[(1/2007)-1]*[(1/2006)-1]*[(1/2005)-1]…*[(1/2)-1]
=[1/2-1][1/3-1][1/4-1]……[1/2006-1][1/2007-1]
=(-1/2)(-2/3)(-3/4)……(-2005/2006)(-2006/2007)
=1/2007
1.1/2+1/2*3+1/3*4+…+1/2006*2007
=1-1/2+1/2-1/3+1/3-1/4+……+1/2006-1/2007
=1-1/2007=2006/2007
2.[(1/2007)-1]*[(1/2006)-1]*[(1/2005)-1]…*[(1/2)-1]
=[1/2-1][1/3-1][1/4-1]……[1/2006-1][1/2007-1]
=(-1/2)(-2/3)(-3/4)……(-2005/2006)(-2006/2007)
=1/2007