Question

[Pham Trong Bach]

Cho hàm số $f\left(x\right)=\ln 2017-\ln \frac{x+1}{x}.$ 

Tính tổng  $S=f\text{'}\left(1\right)+f\text{'}\left(2\right)+f\text{'}\left(3\right)+\mathrm{...}+f\text{'}\left(2018\right).$

A. $S=\frac{4037}{2019}.$

B. $S=\frac{2018}{2019}.$

C. $S=\frac{2017}{2018}.$

D. $S=2018.$

Answer 1

[Cao Minh Tâm]

Đáp án B

ta có  f ' x = − x x + 1 − 1 x 2 = 1 x + 1 x = 1 x − 1 x + 1

⇒ S = 1 − 1 2 + 1 2 − 1 3 + 1 3 − ... + 1 2018 − 1 2019 = 2018 2019