1, 

\(\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}+1\right)...\left(\frac{1}{2017}+1\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{2018}{2017}\)

\(=\frac{2018}{2}=1009\)

2,

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)...\left(\frac{1}{2018}-1\right)\)

\(=\frac{-1}{2}\cdot\frac{-2}{3}\cdot\frac{-3}{4}\cdot...\cdot\frac{-2017}{2018}\)

\(=\frac{-1\cdot2017}{2018}=\frac{-2017}{2018}\)

a) C1

 \(\dfrac{1}{8}\times\dfrac{5}{6}+\dfrac{5}{6}\times\dfrac{2}{3}=\dfrac{5}{6}\times\left(\dfrac{1}{8}+\dfrac{2}{3}\right)=\dfrac{5}{6}\times\dfrac{19}{24}=\dfrac{95}{144}\)

   C2

\(\dfrac{1}{8}\times\dfrac{5}{6}+\dfrac{5}{6}\times\dfrac{2}{3}=\dfrac{5}{48}+\dfrac{10}{18}=\dfrac{95}{144}\)

b) C1

  \(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{3}{4}\times\left(\dfrac{7}{5}-\dfrac{1}{2}\right)=\dfrac{3}{4}\times\dfrac{9}{10}=\dfrac{27}{40}\)

    C2 

   \(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{21}{20}-\dfrac{3}{8}=\dfrac{27}{40}\)

c) C1

 \(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\dfrac{35}{24}\times\dfrac{2}{3}=\dfrac{35}{36}\)

  C2 

  \(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\left(\dfrac{5}{6}\times\dfrac{2}{3}\right)+\left(\dfrac{5}{8}\times\dfrac{2}{3}\right)=\dfrac{5}{9}+\dfrac{5}{12}=\dfrac{35}{36}\)

\(A=1-3+5-7+......-2019+2021-2023\)

\(A=\left(1-3\right)+\left(5-7\right)+....+\left(2021-2023\right)\)

\(A=-2+\left(-2\right)+....+\left(-2\right)\left(506 cặp\right)\)

\(A=-2.506\)

\(A=-1012\)

*) A=(1-3)+(5-7)+....+(2021-2023)

<=> A=-2+(-2)+...+(-2)

Dãy A có (2023-1):2+1=1012 số số hạng 

=> Có 506 số (-2)

=> A=(-2).506=-1012

\(B=1+2-3-4+5+6-7-8+......+2017+2018-2019-2020\)

\(B=\left(1+2-3-4\right)+\left(5+6-7-8\right)+.....+\left(2017+2018-2019-2020\right)\)

\(B=-4+\left(-4\right)+.....+\left(-4\right)\left(505 cặp\right)\)

\(B=-4.505\)

\(B=-2020\)

( -1/7 + 2/7 - 5/11 ) - ( 1/4 - 5/7 )

= ( 1/7 - 5/11 ) - ( 1/4 - 5/7 )

= 1/7 - 5/11 - 1/4 + 5/7

= 6/7 - 5/11 - 1/4 

= 47/308

Cảm ơn bn nhiều

\(a,x:\left(-\frac{15}{28}\right)=\frac{21}{35}\)

                      \(x=\frac{21}{35}\times\left(-\frac{15}{28}\right)\)

                       \(x=-\frac{9}{28}\)

\(b,x-\frac{1}{42}=-\frac{6}{7}\times\frac{5}{7}\)

    \(x-\frac{1}{42}=-\frac{30}{49}\)

                \(x=-\frac{30}{49}+\frac{1}{42}\)

                \(x=-\frac{173}{294}\)

\(c,\left(x-\frac{3}{4}\right):\frac{7}{5}=-\frac{1}{4}\)

               \(x-\frac{3}{4}=-\frac{1}{4}\times\frac{7}{5}\)

               \(x-\frac{3}{4}=-\frac{7}{20}\)

                           \(x=-\frac{7}{20}+\frac{3}{4}\)

                          \(x=\frac{2}{5}\)

a)x:-15/28=21/35

x=21/35.-15/28

x=-9/28

b)x-1/42= -6/7.5/7

x-1/42= -6/7.5/7

x-1/42=-30/49

x=-30/49+1/42

x=-173/294

c)(x-3/4):7/5=-1/4

x-3/4=-1/4.7/5

x-3/4=-7/20

x=-7/20+3/4

x=2/5

có gì sai xin tha thứ giùm nha!

hi hi!!!

=\(\frac{3\left(\frac{1}{1}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{2}{4}+\frac{2}{6}+\frac{2}{8}}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)

=\(\frac{3}{5}+\frac{2\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)=\(\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)

Bằng 2/5