If the image of f(x) is shifted to the right by 1 unit length, and an image of odd function is obtained, then f (x-1) =-f (-x-1) ... (2).

(Because the image moves one unit to the right, the absolute value of the positive coordinate of the X axis decreases by 1, and the absolute value of the negative coordinate of the X axis increases by 1, that is, the odd function definition obtained by image translation is represented by the unknown X).

Because of formula (1), formula (2) can be transformed into f (x-1) =-f (x+1) ... (3).

It can be seen from Formula 3 that f( 1) =-f(3) and f(2) =-f(4).

Then f (1)+f (2)+f (3)+…+f (2011) = f (2010), because all other terms have been eliminated.

f(20 10)= -f(2008)=f(2006)........=f(2)= - 1