f( 1/2)=-f( 1/2+3/2)=-f(2)=- 1

f(2) = 1

f(0) = -f(3/2) = -2

f(3/2) = -f(3/2 + 3/2) = -f(3) = 2

f(3) = -2

From y = f(x-3/4) to odd functions, there are

f(x-3/4) = -f(-x - 3/4)

f(- 1)= f(- 1/4-3/4)=-f( 1/4-3/4)=-f(- 1/2)= 1

f(- 1/2)=-f(- 1/2+3/2)=-f( 1)=- 1

f( 1) = 1

f(x)=-f(x+3/2)= f(x+3/2+3/2)= f(x+3)

So, the order is

f( 1) = 1

f(2) = 1

f(3) = -2

F(n+3) = f(n), that is

1, 1,-2, 1, 1,-2,……

The sum of every three numbers is 1+ 1-2 = 0.

20 15/3 = 67 1……2

therefore

f( 1) + f(2) + f(3) +...+f(20 15)= 67 1 * 0+ 1+ 1 = 2