Question

1) A=\(\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2017^2}\) CM : A < \(\frac{504}{1009}\)

2) Cho a+c=2b; 2bd=c.(b-d) ( b,d \(\ne\) 0) CM \(\frac{a}{b}=\frac{c}{d}\)

3) Tìm x, y

\(\left(x-\frac{2}{5}\right)^{2018}+|y-2|=0\)

Answer 1

Làm bài 1 thui nhé, mấy bài kia dễ tự làm -,- 

\(A=\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2017^2}\)

\(A< \frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2015.2017}\)

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\)

\(=1-\frac{1}{2017}=\frac{1}{2}\left(\frac{1}{2}-\frac{2}{2017}\right)< \frac{1}{2}\left(\frac{1}{2}-\frac{2}{2018}\right)=\frac{1}{2}.\frac{1007}{2018}\)

\(\Rightarrow\)\(2A< \frac{1007}{2018}< \frac{1008}{2018}=\frac{504}{1009}\)\(\Rightarrow\)\(A< \frac{504}{1009}\)

Vậy \(A< \frac{504}{1009}\)

Chúc bạn học tốt ~