\(A=\frac{1}{5}+\left(\frac{1}{14}+\frac{1}{28}+\frac{1}{44}\right)+\left(\frac{1}{61}+\frac{1}{85}+\frac{1}{97}\right)< \frac{1}{5}+3.\frac{1}{14}+3.\frac{1}{61}< \frac{1}{5}+3.\frac{1}{12}+3.\frac{1}{60}\)

\(=\frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\left(ĐPCM\right)\)

Ta có \(\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{44}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}>\frac{1}{14}+\frac{1}{14}+\frac{1}{14}+\frac{1}{14}+\frac{1}{14}+\frac{1}{14}+\frac{1}{14}=\frac{1}{2}\)

                                                                                                 \(>\frac{1}{2}\)

mình có làm tắt mấy bước nhé

Đặt 1/5 + 1/14+1/28 +1/44 + 1/61+1/85+1/97 =A
Ta có : A = 1/5 + ( 1/14+1/28+1/44)+(1/61+1/85+1/97)
A < 1/5 ( 1/14.3)+(1/61.3)
A < 1/5+ 3/14+3/61
A < 1/5 + 3/12+1/20
A < 1/5+1/4+1/20
A < 1/2 ( đpcm)

Cho mik hỏi là 1/97 hay 1/91 vậy

3/61 mà bằng 1/20 à

Đặt 1/5 + 1/14 + 1/28 + 1/44 + 1/61 + 1/85 + 1/97 = A

A = 1/5 + (1/14 + 1/28 + 1/44) + (1/61 + 1/85 + 1/97)

A < 1/5 + (1/14 * 3) + (1/61 * 3)

A < 1/5 + 3/14 + 3/61

A < 1/5 + 3/12 + 3/60

A < 1/2 (đpcm)  

Ta có \(\frac{1}{5}=\frac{1}{5}\)

\(\frac{1}{14}< \frac{1}{10};\frac{1}{28}< \frac{1}{10}\)

\(\frac{1}{44}< \frac{1}{40};\frac{1}{61}< \frac{1}{40};\frac{1}{85}< \frac{1}{40};\frac{1}{97}< \frac{1}{40}\)

\(\Rightarrow\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{44}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}< \frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{40}+\frac{1}{40}+\frac{1}{40}+\frac{1}{40}=\frac{1}{5}+\frac{1}{5}+\frac{1}{10}=\frac{5}{10}=\frac{1}{2}\)\(\Rightarrow A< \frac{1}{2}\)