Let f (x) be an odd function defined on R, and the image of y = f (x) is symmetric with respect to x = 1 / 2, f (1) + F (2) + F (3) + F (4) + F (5)=

The image of y = f (x) is symmetric with respect to the line x = 1 / 2
So f (x) = f (1-x)
F (x) is an odd function defined on R
So f (1-x) = - f (x-1)
f(x)=-f(x-1)
f(x)+f(x-1)=0
f(2)+f(1)=0
f(3)+f(2)=0
f(4)+f(3)=0
f(5)+f(4)=0
So f (1) + F (2) + F (3) + F (4) + F (5) = 0

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