Cho a+b+c= π 2   và cota, cotb, cotc tạo thành cấp số cộng. Gía trị cota.cotc bằng

A. 1  

B. 2   

C. 3   

D. 4

Chứng minh các phân thức sau luôn có nghĩa x 2 + 2 x + 1 x 4 - 2 x 3 - 2 x 2 - 2 x + 4

\(S=\dfrac{2018}{6}+\dfrac{2018}{12}+\dfrac{2018}{20}+......+\dfrac{2018}{2017.2018}\)

\(S=\dfrac{2018}{2.3}+\dfrac{2018}{3.4}+\dfrac{2018}{4.5}+.......+\dfrac{2018}{2017.2018}\)

\(S=2018\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+......+\dfrac{1}{2017.2018}\right)\)

\(S=2018\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+.....+\dfrac{1}{2017}-\dfrac{1}{2018}\right)\)

\(S=2018\left(\dfrac{1}{2}-\dfrac{1}{2018}\right)\)

\(S=2018\cdot\dfrac{504}{1009}\)

\(S=2.504\)

\(S=1008\)

\(\dfrac{-7}{11}=\dfrac{x}{22}\Rightarrow\dfrac{-14}{22}=\dfrac{x}{22}\Rightarrow x=-14\)

\(\dfrac{-5}{11}=\dfrac{x}{33}\Rightarrow\dfrac{-15}{33}=\dfrac{x}{33}\Rightarrow x=-15\)