VT=(1/5+1/6+...+1/9)+(1/10+1/11+...+1/14)+(1/15+1/16+1/17)

VT<(1/5+...+1/5)+(1/10+...+1/10)+(1/15+1/15+1/15)=

=5/5+5/10+3/15=1+1/2+1/5<2

\(A=\dfrac{-\left(6-2n\right)+5}{3-n}=\dfrac{-2\left(3-n\right)+5}{3-n}=-2+\dfrac{5}{3-n}\)

Để A nguyên => 3-n = Ước của 5

\(\Rightarrow3-n=\left\{-5;-1;1;5\right\}\Rightarrow n=\left\{8;4;2;-2\right\}\)

\(A=10^2\times\left[\left(-2\right).10,1-20,21+2.10,11\right]\)

\(=100\times\left[\left(-20,2\right)-20,21+20,22\right]\)

\(=-20,19\times100=-2019\)

\(\dfrac{x+1}{-8}=\dfrac{-2}{x+1}\)
\(\Rightarrow2\left(x+1\right)=\dfrac{-2}{-8}=\dfrac{1}{4}\)
\(\Leftrightarrow x+1=\dfrac{1}{8}\)
\(\Rightarrow x=\dfrac{-7}{8}\)

\(< \dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(=\dfrac{1}{2}-\dfrac{1}{100}< \dfrac{1}{2}\left(đpcm\right)\)

sai đề

\(A=\dfrac{3n-5}{n-4}\) lớn nhất 

\(\Leftrightarrow n-4\) nhỏ nhất

\(\Leftrightarrow n-4=1\)

\(\Leftrightarrow n=5\)

Vậy ...

6/7-1/2:x=-3

         1/2:x=6/7-(-3)

          1/2:x=27/7

                 x=1/2:27/7

                 x=7/54