$\begin{aligned} & \text { Here } \mathrm{k}+2 \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+\mathrm{k}^2+2 \mathrm{k}^2+7 \mathrm{k}^2+\mathrm{k}=1 \\ & \therefore 10 \mathrm{k}^2+9 \mathrm{k}-1=0 \Rightarrow(10 \mathrm{k}-1)(\mathrm{k}+1)=0 \\ & \therefore \mathrm{k}=\frac{1}{10} \quad \ldots(\mathrm{k} \geq 0) \\ & \therefore \mathrm{F}(4)=\mathrm{k}+2 \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}=8 \mathrm{k}=\frac{8}{10}=\frac{4}{5}\end{aligned}$