若f(x)=(x-1/2)^3,则f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=____

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若f(x)=(x-1/2)^3,则f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=____若f(x)=(x-1/2)^3,则f(0.1)+f(0.2)+f(0.3)+...+f(0.9

若f(x)=(x-1/2)^3,则f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=____
若f(x)=(x-1/2)^3,则f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=____

若f(x)=(x-1/2)^3,则f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=____
f(0.1)=(0.1-1/2)^3=-(0.9-1/2)^3=-f(0.9)
f(0.2)=(0.2-1/2)^3=-(0.8-1/2)^3=-f(0.8)
f(0.3)=(0.3-1/2)^3=-(0.7-1/2)^3=-f(0.7)
f(0.4)=(0.4-1/2)^3=-(0.6-1/2)^3=-f(0.6)
f(0.5)=(0.5-1/2)^3=0
所以,f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=0.
.

f(0.1)+f(0.2)+f(0.3)+...+f(0.9)=(-0.4)^3+(-0.3)^3+(-0.2)^3=-0.099

f(x)=-0.4^3-0.3^3-0.2^3-0.1^3+0+0.1^3+0.2^3+0.3^3+0.4^3=0

f(1-x)=-(x-1/2)^3
f(0.1)+f(0.2)+f(0.3)+...+f(0.9)
=f(0.1)+f(0.9)+f(0.2)+f(0.8)+f(0.3)+f(0.7)+f(0.4)+f(0.6)+f(0.5)
=0+0+0+0+0
=0

f(0.1)= - f(0.9),
f(0.2)= - f(0.8),
f(0.3)= - f(0.7),
f(0.4)= - f(0.6),
所以f(0.1)+f(0.2)+……+f(0.9)=f(0.5)=0