Cho hàm số

A

- Hướng dẫn giải

Đáp án A

Ta có:

$$\begin{gathered} f\left(x\right)+f\left(1-x\right)=\frac{2^x}{2^x+2}+\frac{2^{2-x}}{2^{2-x}+2}=\frac{2^x}{2^x+2}+\frac{2^{2-x+x-1}}{2^{2-x+x-1}+2} \\ =\frac{2^x}{2^x+2}+\frac{2^x}{2^x+2}=1 \end{gathered}$$

Khi đó

$$\begin{gathered} f\left(\frac{1}{10}\right)+f\left(\frac{19}{10}\right)+f\left(\frac{2}{10}\right)+f\left(\frac{18}{10}\right)+\mathrm{...}+f\left(0\right)+f\left(1\right) \\ =9+\frac{1}{3}+\frac{1}{2}=\frac{59}{6} \end{gathered}$$