It is known that the image of the function f (x) defined on R is symmetric with respect to the point (- 3 / 4,0) and satisfies f (x) = - f (x + 3 / 2). F (- 1) = 1. F (o) = - 2, Then the value of F (1) + F (2) + F (3) +... + F (2008) is () A.-2 B.-1 C.0 D.1

It is known that the image of the function f (x) defined on R is symmetric with respect to the point (- 3 / 4,0) and satisfies f (x) = - f (x + 3 / 2). F (- 1) = 1. F (o) = - 2, Then the value of F (1) + F (2) + F (3) +... + F (2008) is () A.-2 B.-1 C.0 D.1

F (- 1) = f (- 1 + 3) = f (2), f (0) = f (0 + 3) = f (3), because about - 3 / 4 symmetry, f (- 1) = f (- 1 / 2) = f (- 1 / 2 + 2 / 3) = f (1), f (1) + F (2) + F (3) = 0, f (1 + 3) = f (4), f (2 + 3) = f (5), f (3 + 3) = f (6) ,2008/3=669…… So f (1) + F (2) + F (3) +... + F (2008) = f (1) = f (- 1) = 1