Question

thục hiện phép tính: (1/2+1/3+1/4+.....+1/2017+1/2018)/(2017/1+2016/2+2015/3+.....+2/2016+1/2017)

Các bạn giúp mình nha ! Thank you very much :)

Answer 1

Đặt \(S=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}{\frac{2017}{1}+\frac{2016}{2}+...+\frac{1}{2017}}\)

 Biến đổi mẫu 

\(\frac{2017}{1}+\frac{2016}{2}+...+\frac{1}{2017}\)

\(=\left(2017+1\right)+\left(\frac{2016}{2}+1\right)+...+\left(\frac{1}{2017}+1\right)-2017\)

\(=2018+\frac{2018}{2}+...+\frac{2018}{2017}+\frac{2018}{2018}-2018\)

\(=2018.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)\)

\(\Rightarrow S=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}{2018.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)}=\frac{1}{2018}\)