b = 2006×2008/2007 =(2007- 1)×(2007+ 1)/2007 =(2007×2007- 1)/2007 = 2007- 1/2007
c = 2007×2009/2008 =(2008- 1)×(2008+ 1)/2008 =(2008×2008- 1)/2008 = 2008- 1/2008
Therefore, a < b<c.