1x1/5=1/4(1-1/5)

1/5x1/9=1/4(1/5-1/9)

则有原式=1/4(1-1/5+1/5-1/9+1/9-1/13+……+1/2001-1/2005)

            =1/4(1-1/2005)

            =501/2005