A= 1/3+1/6+1/10+...+1/561

  = 2. (1/6+1/12+1/20+...+1/1122)

  = 2. [1/(2.3) + 1/(3.4) + 1/(4.5) +...+1/(33.34)]

  = 2. ( 1/2 - 1/3 +1/3 - 1/4 + 1/4 - 1/5 +...+ 1/33 - 1/34 )

  =2. (1/2 - 1/34)

  =2. 8/17

  =16/17

Vì 16/17 > 16/18 = 8/9 -> A > 8/9

dễ 4nha

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{2}{7}=\frac{1}{6}\\x+\frac{2}{7}=\frac{-1}{6}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{-5}{42}\\x=\frac{-19}{42}\end{cases}}\)

Vậy ...

 Ta có: \(\left|x+\frac{2}{7}\right|=\frac{1}{6}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{2}{7}=\frac{1}{6}\\x+\frac{2}{7}=-\frac{1}{6}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{6}-\frac{2}{7}=-\frac{5}{42}\\x=-\frac{1}{6}-\frac{2}{7}=-\frac{19}{42}\end{cases}}\)

Vậy \(x\in\left\{-\frac{5}{42};-\frac{19}{42}\right\}\)

~Study well~

20 phút nữa what

2x+2x=4x

3x+6x-7x=2x

5x+45x=50x

\(\frac{1}{\frac{1}{a}+\frac{1}{b}}=\frac{1}{\frac{a+b}{ab}}=\frac{ab}{a+b}\le\frac{\left(a+b\right)^2}{4.\left(a+b\right)}=\frac{a+b}{4}\)

Tương tự \(\frac{1}{\frac{1}{b}+\frac{1}{c}}\le\frac{b+c}{4};\frac{1}{\frac{1}{a}+\frac{1}{c}}\le\frac{c+a}{4}\)

\(\Rightarrow\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{b}+\frac{1}{c}}+\frac{1}{\frac{1}{a}+\frac{1}{c}}\le\frac{a+b}{4}+\frac{b+c}{4}+\frac{c+a}{4}=\frac{2\left(a+b+c\right)}{4}=\frac{a+b+c}{2}\left(đpcm\right)\)