Cho hàm số

B

- Hướng dẫn giải

Đáp án B

ta có $f\text{'}\left(x\right)=-\frac{x}{\left(x+1\right)}\frac{-1}{x^2}=\frac{1}{\left(x+1\right)x}=\frac{1}{x}-\frac{1}{x+1}$

$$\begin{gathered} \Rightarrow S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\mathrm{...}+\frac{1}{2018}-\frac{1}{2019} \\ =\frac{2018}{2019} \end{gathered}$$