\(f\left(x\right)=2^x-x-4\)
\(\rightarrow f\left(0\right)=2^0-0-4=-3\)
\(\rightarrow f\left(1\right)=2^1-1-4=-3\)
\(\rightarrow f\left(2\right)=2^2-2-4=-2\)
\(\rightarrow f\left(3\right)=2^3-3-4=1\)
\(\rightarrow f\left(4\right)=2^4-4-4=8\)
\(\rightarrow f\left(5\right)=2^5-5-4=23\)
\(\rightarrow f\left(6\right)=2^6-6-4=54\)
\(\rightarrow f\left(7\right)=2^7-7-4=117\)
\(\rightarrow f\left(8\right)=2^8-8-4=244\)
Vậy giá trị của tổng là : \(-3+\left(-3\right)+\left(-2\right)+1+8+23+54+117+244=439\)