Question

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

CMR : \(A< \frac{504}{1009}\)

Nhanh lên nhé ! 

Answer 1

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

\(\Rightarrow A< \frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2016.2018}\)

\(\Rightarrow A< \frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(\Rightarrow A< \frac{1}{2}-\frac{1}{2018}=\frac{1009}{2018}-\frac{1}{2018}\)

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

\(\Rightarrow\) \(A< \frac{504}{1009}\left(đpcm\right)\)

Answer 2

Dòng thứ 2 sao lại : \(A< \frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2016.2018}\)vậy bạn 

2.4 ở đâu